1.
Matter
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All the everyday objects that we can bump into, squeeze are ultimately composed of atoms. This atomic matter is in turn made up of interacting subatomic particles -- usually a nucleus of protons and neutrons, a cloud of orbiting electrons. Typically, science considers these composite matter because they have both rest mass and volume. By contrast, massless particles, such as photons, are not considered matter, because they have volume. Nevertheless, their interactions contribute to the effective volume of the composite particles that make up ordinary matter. Matter exists in states: the classical liquid, gas; as well as the more exotic plasma, Bose -- Einstein condensates, fermionic condensates, quark -- gluon plasma. For much of the history of the natural sciences people have contemplated the exact nature of matter. Matter should not be confused with mass, as the two are not quite the same in modern physics. For example, mass is a conserved quantity, which means that its value is unchanging within closed systems. However, matter is not conserved in such systems, although this is not obvious in ordinary conditions on Earth, where matter is approximately conserved. This is also true in the reverse transformation of energy into matter. Different fields of science use the matter in different, sometimes incompatible, ways. Some of these ways are based from a time when there was no reason to distinguish mass and matter. As such, there is no single universally agreed scientific meaning of the word "matter". "matter" is not.
Matter
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Matter
Matter
Matter
Matter
2.
Classical mechanics
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In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the largest subjects in science, engineering and technology. It is also widely known as Newtonian mechanics. Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, well as astronomical objects, such as spacecraft, planets, stars, galaxies. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases and other specific sub-topics. When classical mechanics can not apply, such as at the quantum level with high speeds, quantum field theory becomes applicable. Since these aspects of physics were developed long before the emergence of quantum relativity, some sources exclude Einstein's theory of relativity from this category. However, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most accurate form. Later, more general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. They extend substantially beyond Newton's work, particularly through their use of analytical mechanics. The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles. The motion of a particle is characterized by a small number of parameters: its position, mass, the forces applied to it. Each of these parameters is discussed in turn.
Classical mechanics
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Sir Isaac Newton (1643–1727), an influential figure in the history of physics and whose three laws of motion form the basis of classical mechanics
Classical mechanics
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Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
Classical mechanics
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Hamilton 's greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics.
3.
Second law of motion
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Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between the forces acting upon it, its motion in response to those forces. They can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to investigate the motion of many physical objects and systems. In this way, even a planet can be idealised around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of any particle structure. Newton's laws hold only to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed after Newton's death. In the given mass, acceleration, momentum, force are assumed to be externally defined quantities. Not the only interpretation of the way one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a constant, as, ∑ F = 0 ⇔ d v d t = 0.
Second law of motion
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Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Second law of motion
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Isaac Newton (1643–1727), the physicist who formulated the laws
4.
Continuum mechanics
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The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Research in the area continues today. Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Continuum mechanics deals with physical properties of fluids which are independent of any particular coordinate system in which they are observed. These physical properties are then represented by tensors, which are mathematical objects that have the required property of being independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience. Materials, such as solids, gases, are composed of molecules separated by "empty" space. On a microscopic scale, materials have discontinuities. A continuum is a body that can be continually sub-divided with properties being those of the bulk material. More specifically, the hypothesis/assumption hinges on the concepts of a representative elementary volume and separation of scales based on the Hill -- Mandel condition. The latter then provide a micromechanics basis for finite elements. The levels of SVE and RVE link continuum mechanics to statistical mechanics. The RVE may be assessed only in a limited way via experimental testing: when the constitutive response becomes spatially homogeneous. Specifically for fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made. Consider traffic on a highway -- with just one lane for simplicity.
Continuum mechanics
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Figure 1. Configuration of a continuum body
5.
Kinematics
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Kinematics as a field of study is often referred to as the "geometry of motion" and as such may be seen as a branch of mathematics. The study of the influence of forces acting on masses falls within the purview of kinetics. For further details, see analytical dynamics. Kinematics is used in astrophysics to describe the motion of celestial bodies and collections of such bodies. Kinematic analysis is the process of measuring the kinematic quantities used to describe motion. In addition, kinematics applies algebraic geometry to the study of the mechanical advantage of a mechanical system or mechanism. The term kinematic is the English version of A.M. Ampère's cinématique, which he constructed from the Greek κίνημα kinema, itself derived from κινεῖν kinein. Kinematic and cinématique are related to the French word cinéma, but neither are directly derived from it. Particle kinematics is the study of the trajectory of a particle. The position of a particle is defined to be the coordinate vector from the origin of a coordinate frame to the particle. If the tower is 50 m high, then the coordinate vector to the top of the tower is r=. In the most general case, a three-dimensional coordinate system is used to define the position of a particle. However, if the particle is constrained to move in a surface, a two-dimensional coordinate system is sufficient. All observations in physics are incomplete without those observations being described with respect to a reference frame.
Kinematics
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Each particle on the wheel travels in a planar circular trajectory (Kinematics of Machinery, 1876).
Kinematics
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Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
Kinematics
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Illustration of a four-bar linkage from http://en.wikisource.org/wiki/The_Kinematics_of_Machinery Kinematics of Machinery, 1876
6.
Statics
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The application of Newton's second law to a system gives: F = m a. Where bold font indicates a vector that has magnitude and direction. F is the total of the forces acting on the system, a is the acceleration of the system. The magnitude of the acceleration will be inversely proportional to the mass. The assumption of static equilibrium of a = 0 leads to: F = 0. The summation of forces, one of which might be unknown, allows that unknown to be found. Likewise the application of the assumption of zero acceleration to the summation of moments acting on the system leads to: M = I α = 0. The summation of moments, one of which might be unknown, allows that unknown to be found. These two equations together, can be applied to solve for as many as two loads acting on the system. From Newton's first law, this implies that the net force and torque on every part of the system is zero. See statically determinate. A scalar is a quantity which only has a magnitude, such as temperature. A vector has a direction. Vectors are added using the triangle law. Vectors contain components in orthogonal bases.
Statics
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Example of a beam in static equilibrium. The sum of force and moment is zero.
7.
Statistical mechanics
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A common use of statistical mechanics is in explaining the thermodynamic behaviour of large systems. This branch of statistical mechanics which extends classical thermodynamics is known as statistical thermodynamics or equilibrium statistical mechanics. Statistical mechanics also finds use outside equilibrium. An important subbranch known as statistical mechanics deals with the issue of microscopically modelling the speed of irreversible processes that are driven by imbalances. Examples of such processes include chemical flows of particles and heat. In physics there are two types of mechanics usually examined: quantum mechanics. The statistical ensemble is a distribution over all possible states of the system. In statistical mechanics, the ensemble is a probability distribution over phase points, usually represented as a distribution in a phase space with canonical coordinates. In statistical mechanics, the ensemble is a probability distribution over pure states, can be compactly summarized as a density matrix. These two meanings will be used interchangeably in this article. However the probability is interpreted, each state in the ensemble evolves according to the equation of motion. Thus, the ensemble itself also evolves, as the virtual systems in the ensemble enter another. The evolution is given by the Liouville equation or the von Neumann equation. One special class of ensemble is those ensembles that do not evolve over time. Their condition is known as statistical equilibrium.
Statistical mechanics
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Statistical mechanics
8.
Acceleration
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Acceleration, in physics, is the rate of change of velocity of an object with respect to time. An object's acceleration is the net result of all forces acting on the object, as described by Newton's Second Law. The SI unit for acceleration is metre per second squared. Accelerations add according to the parallelogram law. As a vector, the net force is equal to the product of the object's mass and its acceleration. For example, when a car travels in a straight line at increasing speeds, it is accelerating in the direction of travel. If the car turns, there is an acceleration toward the new direction. When changing direction, we might call this "non-linear acceleration", which passengers might experience as a sideways force. If the speed of the car decreases, this is an acceleration in the opposite direction from the direction of the vehicle, sometimes called deceleration. Passengers may experience deceleration as a force lifting them forwards. Mathematically, there is no separate formula for deceleration: both are changes in velocity. Each of these accelerations might be felt by passengers until their velocity matches that of the car. An object's average acceleration over a period of time is its change in velocity divided by the duration of the period. Mathematically, a ¯ = Δ v Δ t. Instantaneous acceleration, meanwhile, is the limit of the average acceleration over an infinitesimal interval of time.
Acceleration
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Components of acceleration for a curved motion. The tangential component a t is due to the change in speed of traversal, and points along the curve in the direction of the velocity vector (or in the opposite direction). The normal component (also called centripetal component for circular motion) a c is due to the change in direction of the velocity vector and is normal to the trajectory, pointing toward the center of curvature of the path.
Acceleration
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Acceleration is the rate of change of velocity. At any point on a trajectory, the magnitude of the acceleration is given by the rate of change of velocity in both magnitude and direction at that point. The true acceleration at time t is found in the limit as time interval Δt → 0 of Δ v / Δt
9.
Angular momentum
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In physics, angular momentum is the rotational analog of linear momentum. This definition can be applied to each point in continua like solids or fluids, or physical fields. Unlike momentum, angular momentum does depend on where the origin is chosen, since the particle's position is measured from it. The angular momentum of an object can also be connected to the angular velocity ω of the object via the moment of inertia I. Angular momentum is additive; the total angular momentum of a system is the vector sum of the angular momenta. For continua or fields one uses integration. Torque can be defined as the rate of change of angular momentum, analogous to force. Applications include the gyrocompass, control moment gyroscope, Earth's rotation to name a few. In general, conservation does limit the possible motion of a system, but does not uniquely determine what the exact motion is. In quantum mechanics, angular momentum is an operator with quantized eigenvalues. Angular momentum is subject to the Heisenberg uncertainty principle, meaning only one component can be measured with definite precision, the other two cannot. Also, the "spin" of elementary particles does not correspond to literal spinning motion. Angular momentum is a vector quantity that represents the product of a body's rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered a rotational analog of linear momentum. Unlike linear speed, which occurs in a straight line, angular speed occurs about a center of rotation.
Angular momentum
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This gyroscope remains upright while spinning due to the conservation of its angular momentum.
Angular momentum
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An ice skater conserves angular momentum – her rotational speed increases as her moment of inertia decreases by drawing in her arms and legs.
10.
Couple (mechanics)
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In mechanics, a couple is a system of forces with a resultant moment but no resultant force. A better term is force couple or pure moment. Its effect is to create rotation without translation, or more generally without any acceleration of the centre of mass. In rigid body mechanics, force couples are free vectors, meaning their effects on a body are independent of the point of application. The resultant moment of a couple is called a torque. This is not to be confused with the term torque as it is used in physics, where it is merely a synonym of moment. Instead, torque is a special case of moment. Torque has special properties that moment does not have, in particular the property of being independent of reference point, as described below. Definition A couple is a pair of forces, displaced by perpendicular distance or moment. The simplest kind of couple consists of two equal and opposite forces whose lines of action do not coincide. This is called a "simple couple". The forces have a moment called a torque about an axis, normal to the plane of the forces. The SI unit for the torque of the couple is newton metre. The moment of a force is only defined with respect to a certain point P, in general when P is changed, the moment changes. However, the moment of a couple is independent of the P: Any point will give the same moment.
Couple (mechanics)
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Classical mechanics
11.
D'Alembert's principle
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D'Alembert's principle, also known as the Lagrange–d'Alembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, mathematician Jean le Rond d'Alembert. A holonomic constraint depends only on the time. It does not depend on the velocities. More general specification of the irreversibility is required. D'Alembert's contribution was to demonstrate that in the totality of a dynamic system the forces of constraint vanish. That is to say that the generalized forces Q j need not include constraint forces. It is equivalent to the somewhat more cumbersome Gauss's principle of least constraint. The general statement of d'Alembert's principle mentions "the time derivatives of the momenta of the system". To date, nobody has shown that D'Alembert's principle is equivalent to Newton's Second Law. This is true only for some very special cases e.g. rigid body constraints. However, an approximate solution to this problem does exist. Consider Newton's law for a system of i. If virtual displacements are assumed to be in directions that are orthogonal to the constraint forces, the constraint forces do no work. Such displacements are said to be consistent with the constraints.
D'Alembert's principle
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Jean d'Alembert (1717—1783)
D'Alembert's principle
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Free body diagram of a wire pulling on a mass with weight W, showing the d’Alembert inertia “force” ma.
D'Alembert's principle
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Free body diagram depicting an inertia moment and an inertia force on a rigid body in free fall with an angular velocity.
12.
Energy
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In physics, energy is a property of objects which can be transferred to other objects or converted into different forms. It is misleading because energy is not necessarily available to do work. All of the many forms of energy are convertible to other kinds of energy. This means that it is impossible to destroy energy. This creates a limit to the amount of energy that can do work in a cyclic process, a limit called the available energy. Other forms of energy can be transformed in the other direction into thermal energy without such limitations. The total energy of a system can be calculated by adding up all forms of energy in the system. Lifting against gravity performs mechanical work on the object and stores gravitational potential energy in the object. Energy are closely related. With a sensitive enough scale, one could measure an increase in mass after heating an object. Living organisms require available energy to stay alive, such as the energy humans get from food. Civilisation gets the energy it needs from energy resources such as fossil fuels, renewable energy. The processes of Earth's ecosystem are driven by the radiant energy Earth receives from the sun and the geothermal energy contained within the earth. In biology, energy can be thought of as what's needed to keep entropy low. The total energy of a system can be classified in various ways.
Energy
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In a typical lightning strike, 500 megajoules of electric potential energy is converted into the same amount of energy in other forms, mostly light energy, sound energy and thermal energy.
Energy
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Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy.
Energy
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Thomas Young – the first to use the term "energy" in the modern sense.
Energy
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A Turbo generator transforms the energy of pressurised steam into electrical energy
13.
Kinetic energy
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In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done in decelerating from its current speed to a state of rest. In classical mechanics, the kinetic energy of a non-rotating object of mass m traveling at a v is 1 2 m v 2. In relativistic mechanics, this is a good approximation only when v is much less than the speed of light. The standard unit of kinetic energy is the joule. The kinetic has its roots in the Greek word κίνησις kinesis, meaning "motion". The dichotomy between potential energy can be traced back to Aristotle's concepts of actuality and potentiality. Willem's Gravesande of the Netherlands provided experimental evidence of this relationship. Émilie du Châtelet published an explanation. Work in their present scientific meanings date back to the mid-19th century. William Thomson, later Lord Kelvin, is given the credit for coining 1849 -- 51. 1849–51. Energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, rest energy.
Kinetic energy
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The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. When they start rising, the kinetic energy begins to be converted to gravitational potential energy. The sum of kinetic and potential energy in the system remains constant, ignoring losses to friction.
14.
Potential energy
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In physics, potential energy is energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, other factors. The unit for energy in the International System of Units is the joule, which has the symbol J. Potential energy is the stored energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is often associated with restoring forces such as the force of gravity. The action of lifting the mass is performed by an external force that works against the force field of the potential. This work is stored in the field, said to be stored as potential energy. Suppose a ball which it is in h position in height. If the acceleration of free fall is g, the weight of the ball is mg. There are various types of potential energy, each associated with a particular type of force. Thermal energy usually has the potential energy of their mutual positions. Forces derivable from a potential are also called conservative forces. The negative sign provides the convention while work done by the force field decreases potential energy. Common notations for potential energy are U, V, also Ep. Potential energy is closely linked with forces.
Potential energy
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In the case of a bow and arrow, when the archer does work on the bow, drawing the string back, some of the chemical energy of the archer's body is transformed into elastic potential-energy in the bent limbs of the bow. When the string is released, the force between the string and the arrow does work on the arrow. Thus, the potential energy in the bow limbs is transformed into the kinetic energy of the arrow as it takes flight.
Potential energy
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A trebuchet uses the gravitational potential energy of the counterweight to throw projectiles over two hundred meters
Potential energy
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Springs are used for storing elastic potential energy
Potential energy
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Archery is one of humankind's oldest applications of elastic potential energy
15.
Force
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In physics, a force is any interaction that, when unopposed, will change the motion of an object. In other words, a force can cause an object with mass i.e. to accelerate. Force can also be described by intuitive concepts such as a pull. A force has both direction, making it a vector quantity. It is represented by the symbol F. In an extended body, each part usually applies forces on the adjacent parts; the distribution of such forces through the body is the mechanical stress. Pressure is a simple type of stress. Stress usually causes flow in fluids. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about force were eventually corrected by Galileo Galilei and Sir Isaac Newton. With his mathematical insight, Sir Isaac Newton formulated laws of motion that were not improved-on for nearly hundred years. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, weak, gravitational. High-energy physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction. Since antiquity the concept of force has been recognized to the functioning of each of the simple machines.
Force
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Aristotle famously described a force as anything that causes an object to undergo "unnatural motion"
Force
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Forces are also described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything that might cause a mass to accelerate.
Force
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Though Sir Isaac Newton 's most famous equation is, he actually wrote down a different form for his second law of motion that did not use differential calculus.
Force
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Galileo Galilei was the first to point out the inherent contradictions contained in Aristotle's description of forces.
16.
Frame of reference
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In n dimensions, n+1 reference points are sufficient to fully define a reference frame. In Einsteinian relativity, reference frames are used to specify the relationship between the phenomenon or phenomena under observation. A relativistic frame includes the coordinate time, which does not correspond across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all coordinate times are essentially equivalent. The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in Cartesian frame of reference. Sometimes the state of motion is emphasized, in rotating frame of reference. Sometimes the way it transforms to frames considered as related is emphasized in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in microscopic frames of reference. On the other hand, a coordinate system may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. It seems useful to divorce the various aspects of a frame for the discussion below. A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations. Consequently, an observer in an observational frame of reference can choose to employ any coordinate system to describe observations made from that frame of reference. This viewpoint can be found elsewhere well.
Frame of reference
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An observer O, situated at the origin of a local set of coordinates – a frame of reference F. The observer in this frame uses the coordinates (x, y, z, t) to describe a spacetime event, shown as a star.
17.
Impulse (physics)
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In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. Since force is a vector quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, also in the same direction. The SI unit of impulse is the newton second, the dimensionally equivalent unit of momentum is the kilogram meter per second. The corresponding English engineering units are the pound-second and the slug-foot per second. A resultant force causes acceleration and a change in the velocity of the body for as long as it acts. Conversely, a small force applied for a long time produces the same change in momentum—the same impulse—as a larger force applied briefly. This is often called the impulse-momentum theorem. As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied. Impulse has the same units and dimensions as momentum. In the International System of Units, these are kg·m/s = N·s. In English engineering units, they are slug·ft/s = lbf·s. The term "impulse" is also used to refer to a fast-acting force or impact. This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change, is not physically possible.
Impulse (physics)
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A large force applied for a very short duration, such as a golf shot, is often described as the club giving the ball an impulse.
Impulse (physics)
18.
Inertia
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It is the tendency of objects to keep moving in a straight line at constant velocity. Inertia comes from iners, meaning idle, sluggish. Inertia is one of the primary manifestations of mass, a quantitative property of physical systems. Thus, an object will continue moving at its current velocity until some force causes its direction to change. Aristotle concluded that violent motion in a void was impossible. Despite its general acceptance, Aristotle's concept of motion was disputed by notable philosophers over nearly two millennia. For example, Lucretius stated that the "state" of matter was motion, not stasis. This view was strongly opposed by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, where Philoponus did have several supporters who further developed his ideas. In the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridan also maintained that impetus increased with speed; thus, his initial idea of impetus was similar in many ways to the modern concept of momentum. Buridan also believed that impetus could be not only linear, but also circular in nature, causing objects to move in a circle. Buridan's thought was followed up by the Oxford Calculators, who performed various experiments that further undermined the classical, Aristotelian view. Their work in turn was elaborated by Nicole Oresme who pioneered the practice of demonstrating laws of motion in the form of graphs. Benedetti cites the motion of a rock in a sling as an example of the linear motion of objects, forced into circular motion.
Inertia
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Galileo Galilei
19.
Moment of inertia
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It depends on the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems. For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia to the plane. When a body is free to rotate, around an axis, a torque must be applied to change its angular momentum. The amount of torque needed for any given rate of change in momentum is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of metre squared in SI units and pound-square feet in imperial or US units. The moment of inertia depends on how mass will vary depending on the chosen axis. In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, known as a compound pendulum. There is an interesting difference in the moment of inertia appears in planar and spatial movement. The moment of inertia of a rotating flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. If the momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their outstretched divers curl their bodies into a tuck position during a dive, to spin faster. Moment of inertia can be measured using a simple pendulum, because it is the resistance to the rotation caused by gravity. Here r is the distance perpendicular to and from the force to the torque axis. Here F is the tangential component of the net force on the mass.
Moment of inertia
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Tightrope walker Samuel Dixon using the long rod's moment of inertia for balance while crossing the Niagara River in 1890.
Moment of inertia
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Flywheels have large moments of inertia to smooth out mechanical motion. This example is in a Russian museum.
Moment of inertia
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Spinning figure skaters can reduce their moment of inertia by pulling in their arms, allowing them to spin faster due to conservation of angular momentum.
Moment of inertia
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Pendulums used in Mendenhall gravimeter apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth.
20.
Power (physics)
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In physics, power is the rate of doing work. It is the amount of energy consumed per time. Having no direction, it is a quantity. Another traditional measure is horsepower. Being the rate of work, the equation for power can be written: P = W t The integral of power over time defines the work performed. As a physical concept, power requires both a change in a specified time in which the change occurs. This is distinct from the concept of work, only measured in terms of a net change in the state of the physical universe. The power of an electric motor is the product of the torque that the motor generates and the angular velocity of its output shaft. The power involved in moving a vehicle is the product of the velocity of the vehicle. The dimension of power is energy divided by time. The SI unit of power is the watt, equal to one joule per second. Other units of power include foot-pounds per minute. Other units include a relative logarithmic measure with 1 milliwatt as reference; food calories per hour; Btu per hour; and tons of refrigeration. This shows how power is an amount of energy consumed per time. It is the average amount of energy converted per unit of time.
Power (physics)
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Ansel Adams photograph of electrical wires of the Boulder Dam Power Units, 1941–1942
21.
Work (physics)
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The SI unit of work is the joule. Non-SI units of work include the erg, the foot-pound, the foot-poundal, the horsepower-hour. This is approximately the work done lifting a 1 weight from ground level over a person's head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the same distance or by lifting the same weight twice the distance. Work is closely related to energy. Conversely, a decrease in kinetic energy is caused by an equal amount of negative work done by the resultant force. The work of forces generated by a potential function is known as potential energy and the forces are said to be conservative. These formulas demonstrate that work is the energy associated with the action of a force, so work subsequently possesses the physical dimensions, units, of energy. The work/energy principles discussed here are identical to Electric work/energy principles. Constraint forces determine the movement of components in a system, constraining the object within a boundary. Constraint forces ensure the velocity in the direction of the constraint is zero, which means the constraint forces do not perform work on the system. This only applies for a single particle system. In an Atwood machine, the rope does work on each body, but keeping always the virtual work null. There are, however, cases where this is not true. This force does zero work because it is perpendicular to the velocity of the ball.
Work (physics)
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A baseball pitcher does positive work on the ball by applying a force to it over the distance it moves while in his grip.
Work (physics)
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A force of constant magnitude and perpendicular to the lever arm
Work (physics)
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Gravity F = mg does work W = mgh along any descending path
Work (physics)
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Lotus type 119B gravity racer at Lotus 60th celebration.
22.
Momentum
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In classical mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object, quantified in kilogram-meters per second. It is dimensionally equivalent to the product of force and time, quantified in newton-seconds. Newton's second law of motion states that the change in linear momentum of a body is equal to the net impulse acting on it. If the truck were lighter, or moving more slowly, then it would therefore require less impulse to start or stop. Linear momentum is also a conserved quantity, meaning that if a closed system is not affected by external forces, its linear momentum can not change. In classical mechanics, conservation of linear momentum is implied by Newton's laws. With appropriate definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory, general relativity. It is ultimately an expression of the fundamental symmetries of space and time, that of translational symmetry. Linear momentum depends on frame of reference. Observers in different frames would find different values of linear momentum of a system. But each would observe that the value of linear momentum does not change provided the system is isolated. Momentum has a direction well as magnitude. Quantities that have both a direction are known as vector quantities. Because momentum has a direction, it can be used to predict the resulting direction of objects after they collide, well as their speeds. Below, the basic properties of momentum are described in one dimension.
Momentum
–
In a game of pool, momentum is conserved; that is, if one ball stops dead after the collision, the other ball will continue away with all the momentum. If the moving ball continues or is deflected then both balls will carry a portion of the momentum from the collision.
23.
Space
–
Space is the boundless three-dimensional extent in which objects and events have relative position and direction. The concept of space is considered to be to an understanding of the physical universe. However, disagreement continues between philosophers over whether it is itself an entity, part of a conceptual framework. Many of these philosophical questions were discussed in the Renaissance and then reformulated in the 17th century, particularly during the early development of classical mechanics. In Isaac Newton's view, space was absolute -- in the sense that it existed independently of whether there was any matter in the space. Kant referred to the experience of "space" as being a subjective "pure a priori form of intuition". In the 20th centuries mathematicians began to examine geometries that are non-Euclidean, in which space is conceived as curved, rather than flat. According to Albert Einstein's theory of general relativity, space around gravitational fields deviates from Euclidean space. Experimental tests of general relativity have confirmed that non-Euclidean geometries provide a better model for the shape of space. In the seventeenth century, the philosophy of time emerged as a central issue in epistemology and metaphysics. At its heart, the English physicist-mathematician, set out two opposing theories of what space is. Unoccupied regions are those that could have objects in them, thus spatial relations with other places. Space could be thought in a similar way to the relations between family members. Although people in the family are related to one another, the relations do not exist independently of the people. According to the principle of sufficient reason, any theory of space that implied that there could be these two possible universes must therefore be wrong.
Space
–
Gottfried Leibniz
Space
–
A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space.
Space
–
Isaac Newton
Space
–
Immanuel Kant
24.
Speed
–
In everyday use and in kinematics, the speed of an object is the magnitude of its velocity; it is thus a scalar quantity. Speed has the dimensions of distance divided by time. For air and marine travel the knot is commonly used. Matter cannot quite reach the speed of light, as this would require an infinite amount of energy. In relativity physics, the concept of rapidity replaces the classical idea of speed. The time it takes. Galileo defined speed as the distance covered per unit of time. In equation form, this is v = d t, t is time. A cyclist who covers 30 metres in a time of 2 seconds, for example, has a speed of 15 metres per second. Objects in motion often have variations in speed. If s is the length of the path travelled until t, the speed equals the time derivative of s: v = d s d t. In the special case where the velocity is constant, this can be simplified to v = s / t. The average speed over a finite interval is the total distance travelled divided by the time duration. Assumed constant during a very short period of time, is called instantaneous speed. By looking at a speedometer, one can read the instantaneous speed of a car at any instant.
Speed
–
Speed can be thought of as the rate at which an object covers distance. A fast-moving object has a high speed and covers a relatively large distance in a given amount of time, while a slow-moving object covers a relatively small amount of distance in the same amount of time.
25.
Time
–
Time is the indefinite continued progress of existence and events that occur in apparently irreversible succession from the past through the present to the future. Time is often referred to as the fourth dimension, along with the three spatial dimensions. Nevertheless, diverse fields such as business, industry, sports, the performing arts all incorporate some notion of time into their respective measuring systems. Two contrasting viewpoints on time divide prominent philosophers. One view is that time is part of the fundamental structure of the universe -- a independent of events, in which events occur in sequence. Hence it is sometimes referred to as Newtonian time. Time in physics is unambiguously operationally defined as "what a clock reads". Time is one of International System of Quantities. Time is used to define other quantities—such as velocity—so defining time in terms of such quantities would result in circularity of definition. Temporal measurement was a prime motivation in navigation and astronomy. Periodic motion have long served as standards for units of time. Currently, the international unit of the second, is defined by measuring the electronic transition frequency of caesium atoms. In day-to-day life, the clock is consulted than a day whereas the calendar is consulted for periods longer than a day. Increasingly, electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of a specified event as to date is obtained by counting from a fiducial epoch -- a central reference point.
Time
–
The flow of sand in an hourglass can be used to keep track of elapsed time. It also concretely represents the present as being between the past and the future.
Time
Time
–
Horizontal sundial in Taganrog
Time
–
A contemporary quartz watch
26.
Torque
–
Torque, moment, or moment of force is the tendency of a force to rotate an object around an axis, fulcrum, or pivot. Just as a force is a pull, a torque can be thought of as a twist to an object. Loosely speaking, torque is a measure of the force on an object such as a bolt or a flywheel. The symbol for torque is typically the lowercase Greek letter tau. When it is called moment of force, it is commonly denoted by M. The SI unit for torque is the metre. For more on the units of torque, see Units. This article follows US physics terminology in its use of the torque. In the UK and in US mechanical engineering, this is called moment of force, usually shortened to moment. Torque is defined mathematically as the rate of change of momentum of an object. The definition of torque states that the moment of inertia of an object are changing. For a rotational force applied to a shaft causing acceleration, such as a drill bit accelerating from rest, results in a moment called a torque. Similarly with any couple on an object that has no change to its angular momentum, such moment is also not called a torque. The concept of torque, also called couple, originated with the studies of Archimedes on levers. The torque was apparently introduced into English scientific literature by James Thomson, the brother of Lord Kelvin, in 1884.
Torque
27.
Velocity
–
The velocity of an object is the rate of change of its position with respect to a frame of reference, is a function of time. Velocity is equivalent to a specification of its speed and direction of motion. Velocity is an important concept in kinematics, the branch of classical mechanics that describes the motion of bodies. Velocity is a physical quantity; both direction are needed to define it. For example, "5 metres per second" is a scalar, whereas "5 metres per second east" is a vector. If there is a change in both, then the object has a changing velocity and is said to be undergoing an acceleration. To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant velocity means motion in a straight line at a constant speed. Hence, the car is considered to be undergoing an acceleration. Speed describes only how fast an object is moving, whereas velocity gives both how fast and in what direction the object is moving. If a car is said to travel at 60 km/h, its speed has been specified. However, if the car is said to move at 60 km/h to the north, its velocity has now been specified. The big difference can be noticed when we consider movement around a circle. Average velocity can be calculated as: v ¯ = Δ x Δ t. The average velocity is always less than or equal to the average speed of an object.
Velocity
–
As a change of direction occurs while the cars turn on the curved track, their velocity is not constant.
28.
Virtual work
–
Virtual work arises in the application of the principle of least action to the study of forces and movement of a mechanical system. The work of a force acting on a particle as it moves along a displacement will be different for different displacements. Among all the possible displacements that a particle may follow, called virtual displacements, one will minimize the action. This displacement is therefore the displacement followed according to the principle of least action. The work of a force on a particle along a virtual displacement is known as the virtual work. The principle of virtual work had always been used in the study of statics. It was used by the Greeks, Renaissance Italians. Working with Leibnizian concepts, Johann Bernoulli made explicit the concept of infinitesimal displacement. He was able to solve problems for both rigid bodies well as fluids. His idea was to convert a dynamical problem by introducing inertial force. Consider a particle that moves along a path, described by a function r from point A, where r, to point B, where r. The δr satisfies the requirement δr = δr = 0. The components of the variation, δr1, δr3, are called virtual displacements. This can be generalized to an arbitrary mechanical system defined by the generalized coordinates qi, i = 1... n. In which case, the variation of the trajectory qi is defined by the virtual displacements δqi, i = 1... n.
Virtual work
–
This is an engraving from Mechanics Magazine published in London in 1824.
Virtual work
–
Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train
29.
Newton's laws of motion
–
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, its motion in response to those forces. They have been expressed in several different ways, over nearly three centuries, can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given mass, force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F = 0 ⇔ d v d t = 0.
Newton's laws of motion
–
Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's laws of motion
–
Isaac Newton (1643–1727), the physicist who formulated the laws
30.
Analytical mechanics
–
In theoretical physics and mathematical physics, analytical mechanics, or theoretical mechanics is a collection of closely related alternative formulations of classical mechanics. It was onward, after Newtonian mechanics. A scalar is a quantity, whereas a vector is represented by direction. The equations of motion are derived by some underlying principle about the scalar's variation. Analytical mechanics takes advantage of a system's constraints to solve problems. The formalism is well suited to arbitrary choices of coordinates, known in the context as generalized coordinates. Two dominant branches of analytical mechanics are Hamiltonian mechanics. There are other formulations such as Hamilton -- Appell's equation of motion. All equations in any formalism, can be derived from the widely applicable result called the principle of least action. One result is a statement which connects conservation laws to their associated symmetries. Analytical mechanics is not more general than Newtonian mechanics. Rather it is a collection of equivalent formalisms which have broad application. Analytical mechanics is used widely, from fundamental physics to applied mathematics, particularly theory. The methods of analytical mechanics apply with a finite number of degrees of freedom. They can be modified to describe continuous fluids, which have infinite degrees of freedom.
Analytical mechanics
–
As the system evolves, q traces a path through configuration space (only some are shown). The path taken by the system (red) has a stationary action (δ S = 0) under small changes in the configuration of the system (δ q).
31.
Lagrangian mechanics
–
Lagrangian mechanics is a reformulation of classical mechanics, introduced by the Italian-French mathematician and astronomer Joseph-Louis Lagrange in 1788. No new physics is introduced in Lagrangian mechanics compared to Newtonian mechanics. Newton's laws can include non-conservative forces like friction; however, they must include constraint forces explicitly and are best suited to Cartesian coordinates. Lagrangian mechanics is ideal for systems with conservative forces and for bypassing constraint forces in any coordinate system. Lagrangian mechanics also reveals conserved quantities and their symmetries in a direct way, as a special case of Noether's theorem. Lagrangian mechanics is important not just for its broad applications, but also for its role in advancing deep understanding of physics. It can also be applied to other systems by analogy, for instance to coupled electric circuits with inductances and capacitances. Lagrangian mechanics is widely used to solve mechanical problems in physics and engineering when Newton's formulation of classical mechanics is not convenient. Lagrangian mechanics applies to the dynamics of particles, fields are described using a Lagrangian density. Lagrange's equations are also used in optimisation problems of dynamic systems. In mechanics, Lagrange's equations of the second kind are used much more than those of the first kind. Suppose we have a bead sliding around on a wire, or a swinging simple pendulum, etc. This choice eliminates the need for the constraint force to enter into the resultant system of equations. There are fewer equations since one is not directly calculating the influence of the constraint on the particle at a given moment. For a system of N point particles with masses m1, m2... mN, each particle has a position vector, denoted r1, r2... rN.
Lagrangian mechanics
–
Joseph-Louis Lagrange (1736—1813)
Lagrangian mechanics
–
Isaac Newton (1642—1726)
Lagrangian mechanics
–
Jean d'Alembert (1717—1783)
32.
Routhian mechanics
–
In analytical mechanics, a branch of theoretical physics, Routhian mechanics is a hybrid formulation of Lagrangian mechanics and Hamiltonian mechanics developed by Edward John Routh. Correspondingly, the Routhian is the function which replaces both the Lagrangian and Hamiltonian functions. The difference between the Lagrangian, Hamiltonian, Routhian functions are their variables. The Routhian differs from these functions in that some coordinates are chosen to have corresponding generalized velocities, the rest to have corresponding generalized momenta. This choice is arbitrary, can be done to simplify the problem. In each case the Lagrangian and Hamiltonian functions are replaced by a single function, the Routhian. The Lagrangian equations are powerful results, used frequently in theory and practice, since the equations of motion in the coordinates are easy to set up. However, if cyclic coordinates occur there will still be equations to solve for all the coordinates, including the cyclic coordinates despite their absence in the Lagrangian. Overall fewer equations need to be solved compared to the Lagrangian approach. As with the rest of analytical mechanics, Routhian mechanics is completely equivalent to Newtonian mechanics, all other formulations of classical mechanics, introduces no new physics. It offers an alternative way to solve mechanical problems. The velocities dqi/dt are expressed as functions of their corresponding momenta by inverting their defining relation. In this context, pi is said to be the momentum "canonically conjugate" to qi. The choice of which n coordinates are to have corresponding momenta, out of the n + s coordinates, is arbitrary. The above is used by Landau and Lifshitz, Goldstein.
Routhian mechanics
–
Edward John Routh, 1831–1907.
33.
Damping
–
If a frictional proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the coefficient, the system can: Oscillate with a frequency lower than in the non-damped case, an amplitude decreasing with time. Decay without oscillations. The solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called "critically damped." If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator. Mechanical examples include acoustical systems. Other analogous systems include harmonic oscillators such as RLC circuits. Harmonic oscillators are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal waves. A harmonic oscillator is an oscillator, neither driven nor damped. The motion is periodic, repeating itself in a sinusoidal fashion with A. The position at a given t also depends on the phase, φ, which determines the starting point on the sine wave. The acceleration of a simple harmonic oscillator oscillate with the same frequency as the position but with shifted phases. The velocity is maximum for zero displacement, while the acceleration is in the opposite direction as the displacement. The potential energy stored in a harmonic oscillator at position x is U = 1 2 k x 2.
Damping
–
Mass attached to a spring and damper.
34.
Damping ratio
–
In engineering, the damping ratio is a dimensionless measure describing how oscillations in a system decay after a disturbance. Many systems exhibit oscillatory behavior when they are disturbed from their position of static equilibrium. A mass suspended from a spring, for example, might, if released, bounce up and down. On each bounce, the system overshoots it. Sometimes losses can cause the oscillations to gradually decay in amplitude towards zero or attenuate. The damping ratio is a measure of describing how rapidly the oscillations decay from one bounce to the next. Where the spring–mass system is completely lossless, the mass would oscillate indefinitely, with each bounce of equal height to the last. This hypothetical case is called undamped. This case is called overdamped. Commonly, the mass tends overshooting again. With each overshoot, the oscillations die towards zero. This case is called underdamped. This case is called critical damping. The key difference between critical overdamping is that, in critical damping, the system returns to equilibrium in the minimum amount of time. The damping ratio is a parameter, usually denoted by ζ, that characterizes the response of a second order ordinary differential equation.
Damping ratio
–
The effect of varying damping ratio on a second-order system.
35.
Displacement (vector)
–
A displacement is a vector, the shortest distance from the initial to the final position of a point P. It quantifies both the distance and direction of an imaginary motion along a straight line from the initial position to the final position of the point. The velocity then is distinct from the instantaneous speed, the time rate of change of the distance traveled along a specific path. The velocity may be equivalently defined as the rate of change of the vector. For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity. In dealing with the motion of a rigid body, the term displacement may also include the rotations of the body. In this case, the displacement of a particle of the body is called linear displacement, while the rotation of the body is called angular displacement. For a vector s, a function of t, the derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, other sciences and engineering disciplines. By extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the original displacement function. The fourth derivative is called jounce, the sixth pop. Equipollence Position vector Affine space
Displacement (vector)
–
Displacement versus distance traveled along a path
36.
Equations of motion
–
In mathematical physics, equations of motion are equations that describe the behaviour of a physical system in terms of its motion as a function of time. The most general choice are generalized coordinates which can be any convenient variables characteristic of the physical system. The functions are replaced by curved spaces in relativity. If the dynamics of a system is known, the equations are the solutions to the differential equations describing the motion of the dynamics. There are two main descriptions of motion: kinematics. Dynamics is general, since momenta, energy of the particles are taken into account. In this instance, sometimes the term refers to the differential equations that the system satisfies, sometimes to the solutions to those equations. However, kinematics is simpler as it concerns time. Equations of motion can therefore be grouped under these main classifiers of motion. In all cases, the main types of motion are translations, rotations, any combinations of these. Solving the equation will lead to a general solution with arbitrary constants, the arbitrariness corresponding to a family of solutions. A particular solution can be obtained by setting the initial values, which fixes the values of the constants. Euclidean vectors in 3D are denoted throughout in bold. The initial conditions are given by the constant values at t r, r ˙. The solution r with specified initial values, describes the system for all times t after t = 0.
Equations of motion
–
Kinematic quantities of a classical particle of mass m: position r, velocity v, acceleration a.
37.
Fictitious force
–
The F does not arise from any physical interaction between two objects, but rather from the acceleration a of the non-inertial reference frame itself. As stated by Iro: Such an additional force due to nonuniform relative motion of two reference frames is called a pseudo-force. Assuming Newton's second law in the F = ma, fictitious forces are always proportional to the mass m. A fictitious force on an object arises when the frame of reference used to describe the object's motion is accelerating compared to a non-accelerating frame. As a frame can accelerate in any arbitrary way, so can fictitious forces be as arbitrary. Gravitational force would also be a fictitious force based upon a model in which particles distort spacetime due to their mass. The surface of the Earth is a rotating frame. The Euler force is typically ignored because the variations in the velocity of the rotating Earth surface are usually insignificant. They can be detected under careful conditions. For example, Léon Foucault was able to show that the Coriolis force results from the Earth's rotation using the Foucault pendulum. Other accelerations also give rise to fictitious forces, as described below. An example of the detection of a rotating reference frame is the precession of a Foucault pendulum. In the non-inertial frame of the Earth, the fictitious Coriolis force is necessary to explain observations. In an inertial frame outside the Earth, no fictitious force is necessary. Figure 1 shows an accelerating car.
Fictitious force
38.
Friction
–
Friction is the force resisting the relative motion of solid surfaces, fluid layers, material elements sliding against each other. There are several types of friction: Dry friction resists lateral motion of two solid surfaces in contact. Dry friction is subdivided into kinetic friction between moving surfaces. Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other. Lubricated friction is a case of fluid friction where a fluid separates two solid surfaces. Friction is a component of drag, the force resisting the motion of a fluid across the surface of a body. Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation. When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear, which damage to components. Friction is a component of the science of tribology. Friction is not itself a fundamental force. Dry friction arises from a combination of inter-surface adhesion, surface roughness, surface contamination. Friction is a non-conservative force - work done against friction is path dependent.
Friction
–
When the mass is not moving, the object experiences static friction. The friction increases as the applied force increases until the block moves. After the block moves, it experiences kinetic friction, which is less than the maximum static friction.
39.
Harmonic oscillator
–
If a frictional force proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the coefficient, the system can: Oscillate lower in an amplitude decreasing with time. Decay to the equilibrium position, without oscillations. The boundary solution between an underdamped oscillator and an overdamped oscillator occurs at a particular value of the friction coefficient and is called "critically damped." If an external time dependent force is present, the harmonic oscillator is described as a driven oscillator. Mechanical examples include pendulums, masses connected to springs, acoustical systems. Other analogous systems include electrical harmonic oscillators such as RLC circuits. Harmonic oscillators occur widely in nature and are exploited in many manmade devices, such as clocks and radio circuits. They are the source of virtually all sinusoidal vibrations and waves. A simple harmonic oscillator is an oscillator, neither driven nor damped. The motion is periodic, repeating itself in a sinusoidal fashion with constant amplitude, A. The position at a given time t also depends on the phase, φ, which determines the starting point on the sine wave. The velocity and acceleration of a simple harmonic oscillator oscillate with the same frequency as the position but with shifted phases. The velocity is maximum for zero displacement, while the acceleration is in the opposite direction as the displacement. The potential energy stored in a simple harmonic oscillator at position x is U = 1 2 k x 2.
Harmonic oscillator
–
Another damped harmonic oscillator
Harmonic oscillator
–
Dependence of the system behavior on the value of the damping ratio ζ
40.
Inertial frame of reference
–
The physics of a system in an inertial frame have no causes external to the system. Measurements in one inertial frame can be converted to measurements in another by a simple transformation. Systems in non-inertial frames in general relativity don't have external causes because of the principle of geodesic motion. Physical laws take the same form in all inertial frames. For example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating. Someone rotating with the Earth must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion. Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force. The motion of a body can only be described relative to something else -- a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Indeed, an intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form. In an inertial frame, the law of inertia, is satisfied: Any free motion has direction.
Inertial frame of reference
–
Figure 1: Two frames of reference moving with relative velocity. Frame S' has an arbitrary but fixed rotation with respect to frame S. They are both inertial frames provided a body not subject to forces appears to move in a straight line. If that motion is seen in one frame, it will also appear that way in the other.
41.
Mechanics of planar particle motion
–
This article describes a particle in planar motion when observed from non-inertial reference frames. See centrifugal force, two-body problem, Kepler's laws of planetary motion. Those problems fall from given laws of force. The Lagrangian approach to fictitious forces is introduced. Unlike real forces such as electromagnetic forces, fictitious forces do not originate from physical interactions between objects. This allows us to detect experimentally the non-inertial nature of a system. Pretend you are in an inertial frame. Elaboration of some citations on the subject follow. Examples are Cartesian coordinates, polar coordinates and curvilinear coordinates. The corresponding set of axes, sharing the rigid motion of the frame R, can be considered to give a physical realization of R. In traditional developments of general relativity it has been customary not to distinguish between two quite distinct ideas. The first is the notion of a coordinate system, understood simply to events in spacetime neighborhoods. Or as seen from a rotating frame. A time-dependent description of observations does not change the frame of reference in which the observations are recorded. In discussion of a particle moving in an inertial frame of reference one can identify the centripetal and tangential forces.
Mechanics of planar particle motion
–
The arc length s(t) measures distance along the skywriter's trail. Image from NASA ASRS
Mechanics of planar particle motion
Mechanics of planar particle motion
–
Figure 2: Two coordinate systems differing by a displacement of origin. Radial motion with constant velocity v in one frame is not radial in the other frame. Angular rate, but
42.
Motion (physics)
–
In physics, motion is a change in position of an object over time. Motion is typically described in terms of displacement, distance, velocity, acceleration, speed. An object's motion can not change unless it is acted by a force, as described. Momentum is a quantity, used for measuring motion of an object. As there is no absolute frame of reference, absolute motion cannot be determined. Thus, everything in the universe can be considered to be moving. One can also speak of motion of boundaries. So, the motion in general signifies a continuous change in the configuration of a physical system. In physics, motion is described through two sets of apparently contradictory laws of mechanics. Motions of familiar objects in the universe are described by classical mechanics. Whereas the motion of sub-atomic objects is described by quantum mechanics. It is one of the oldest and largest in science, engineering, technology. Classical mechanics is fundamentally based on Newton's laws of motion. These laws describe the relationship between the forces acting on the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 1687.
Motion (physics)
–
Motion involves a change in position, such as in this perspective of rapidly leaving Yongsan Station.
43.
Newton's law of universal gravitation
–
This is a general physical law derived from empirical observations by what Isaac Newton called induction. It is a part of classical mechanics and was formulated in Newton's work Philosophiæ Naturalis Principia Mathematica, first published on 5 July 1687. In modern language, the law states: Every mass attracts every other mass by a force pointing along the line intersecting both points. The force is proportional to the product of the two masses and inversely proportional to the square of the distance between them. The first test of Newton's theory of gravitation between masses in the laboratory was the Cavendish experiment conducted by the British scientist Henry Cavendish in 1798. It took place 111 years after the publication of Newton's Principia and approximately 71 years after his death. Newton's law of gravitation resembles Coulomb's law of electrical forces, used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has the constant in place of the constant. At the same time Hooke agreed that "the Demonstration of the Curves generated thereby" was wholly Newton's. In this way, the question arose as to what, if anything, Newton owed to Hooke. This is a subject extensively discussed since that time and on which some points, outlined below, continue to excite controversy. Hooke's statements up to 1674 made no mention, however, that an inverse square law applies or might apply to these attractions. Hooke's gravitation was also not yet universal, though it approached universality more closely than previous hypotheses. He also did not provide accompanying evidence or mathematical demonstration.
Newton's law of universal gravitation
44.
Relative velocity
–
We begin with relative motion in the classical, that all speeds are much less than the speed of light. This limit is associated with the Galilean transformation. The figure shows a man on top of a train, at the back edge. At 1:00 pm he begins to walk forward at a walking speed of 10 km/hr. The train is moving at 40 km/hr. The figure depicts the train at two different times: first, when the journey began, also one hour later at 2:00 pm. The figure suggests that the man is 50 km from the starting point after having traveled for one hour. This, by definition, is 50 km/hour, which suggests that the prescription for calculating relative velocity in this fashion is to add the two velocities. V → M | T is the velocity of the Man relative to the Train. V → T | E is the velocity of the Train relative to Earth. The figure shows two objects moving at constant velocity. The difference between the two displacement vectors, r → B − r → A, represents the location of B as seen from A. To construct a theory of relative motion consistent with the theory of special relativity, we must adopt a different convention. Recall that v is the motion of a stationary object in the primed frame, as seen from the unprimed frame. Hence relative speed is symmetrical.
Relative velocity
–
Relative velocities between two particles in classical mechanics.
45.
Rigid body
–
In physics, a rigid body is an idealization of a solid body in which deformation is neglected. In other words, the distance between any two given points of a rigid body remains constant in time regardless of external forces exerted on it. For instance, in quantum mechanics molecules are often seen as rigid bodies.. The position of a rigid body is the position of all the particles of which it is composed. If the body is rigid, it is sufficient to describe the position of at least three non-collinear particles. This makes it possible to reconstruct the position of all the other particles, provided that their time-invariant position relative to the three selected particles is known. Typically a different, mathematically equivalent approach is used. Thus, the position of a rigid body has two components: linear and angular, respectively. This reference point may define the origin of a coordinate system fixed to the body. In general, when a rigid body moves, both its position and orientation vary with time. In the kinematic sense, these changes are referred to as translation and rotation, respectively. Indeed, the position of a rigid body can be viewed starting from a hypothetic position. Velocity are measured with respect to a frame of reference. The linear velocity of a rigid body is a quantity, equal to the rate of change of its linear position. Thus, it is the velocity of a reference point fixed to the body.
Rigid body
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The position of a rigid body is determined by the position of its center of mass and by its attitude (at least six parameters in total).
46.
Rigid body dynamics
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Rigid-body dynamics studies the movement of systems of interconnected bodies under the action of external forces. This excludes plastic behavior. The solution of rigid body dynamics is an important tool in the computer simulation of mechanical systems. If a system of particles moves parallel to a fixed plane, the system is said to be constrained to movement. In this case, Newton's laws for a rigid system of Pi, i = 1... N, simplify because there is no movement in the k direction. Several methods to describe orientations of a rigid body in three dimensions have been developed. They are summarized in the following sections. The first attempt to represent an orientation is attributed to Leonhard Euler. The values of these three rotations are called Euler angles. These are three angles, also known as yaw, roll, Navigation angles and Cardan angles. In engineering they are usually referred to as Euler angles. Euler also realized that the composition of two rotations is equivalent to a single rotation about a fixed axis. Therefore, the composition of the former three angles has to be equal to only one rotation, whose axis was complicated to calculate until matrices were developed. Therefore, any orientation can be represented by a vector that leads to it from the reference frame. When used to represent an orientation, the vector is commonly called orientation vector, or attitude vector.
Rigid body dynamics
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Human body modelled as a system of rigid bodies of geometrical solids. Representative bones were added for better visualization of the walking person.
Rigid body dynamics
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Movement of each of the components of the Boulton & Watt Steam Engine (1784) is modeled by a continuous set of rigid displacements
47.
Vibration
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Vibration is a mechanical phenomenon whereby oscillations occur about an equilibrium point. The word comes from Latin vibrationem. The oscillations may be periodic, such as the motion of a pendulum—or random, such as the movement of a tire on a gravel road. In many cases, however, vibration is wasting energy and creating unwanted sound. For example, the vibrational motions of engines, any mechanical device in operation are typically unwanted. Such vibrations could be caused by imbalances in the rotating parts, the meshing of gear teeth. Careful designs usually minimize unwanted vibrations. The studies of vibration are closely related. Pressure waves, are generated by vibrating structures; these pressure waves can also induce the vibration of structures. Hence, attempts to reduce noise are often related to issues of vibration. Free vibration occurs when a mechanical system is allowed to vibrate freely. Examples of this type of vibration are pulling a child back on a swing and letting go, or letting it ring. The mechanical system damps down to motionlessness. Forced vibration is when a time-varying disturbance is applied to a mechanical system. The disturbance can be a periodic and steady-state input, a random input.
Vibration
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Car Suspension: designing vibration control is undertaken as part of acoustic, automotive or mechanical engineering.
Vibration
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One of the possible modes of vibration of a circular drum (see other modes).
48.
Circular motion
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In physics, circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. Without this acceleration, the object would move according to Newton's laws of motion. In physics, circular motion describes the motion of a body traversing a circular path at constant speed. Since the body describes circular motion, its distance from the axis of rotation remains constant at all times. Though the body's speed is constant, its velocity is not constant: a vector quantity, depends on both the body's speed and its direction of travel. This changing velocity indicates the presence of an acceleration; this centripetal acceleration is of constant magnitude and directed at all times towards the axis of rotation. This acceleration is, in turn, directed towards the axis of rotation. Note: The magnitude of the angular velocity is the angular speed. For motion in a circle of radius r, the circumference of the circle is C = 2π r. The axis of rotation is shown as a vector perpendicular to the plane of the orbit and with a magnitude ω = dθ / dt. The direction of ω is chosen using the right-hand rule. In the simplest case the mass and radius are constant.
Circular motion
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Figure 1: Velocity v and acceleration a in uniform circular motion at angular rate ω; the speed is constant, but the velocity is always tangent to the orbit; the acceleration has constant magnitude, but always points toward the center of rotation
49.
Centripetal force
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A centripetal force is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre". In Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path. The mathematical description was derived in 1659 by the Dutch physicist Christiaan Huygens. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle. The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. Expressed using the orbital period T for one revolution of the circle, ω = 2 π T the equation becomes F = m r 2. The rope example is an example involving a'pull' force. Newton's idea of a centripetal force corresponds to what is nowadays referred to as a central force. In this case, the magnetic force is the centripetal force that acts towards the helix axis. Below are three examples of increasing complexity, with derivations of the formulas governing velocity and acceleration.
Centripetal force
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A body experiencing uniform circular motion requires a centripetal force, towards the axis as shown, to maintain its circular path.
50.
Centrifugal force
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The term has sometimes also been used for the force, a reaction to a centripetal force. All measurements of position and velocity must be made relative to some frame of reference. An inertial frame of reference is one, not accelerating. In terms of an inertial frame of reference, the centrifugal force does not exist. All calculations can be performed using only Newton's laws of motion and the real forces. In its current usage the term'centrifugal force' has no meaning in an inertial frame. In an inertial frame, an object that has no forces acting on it travels in a straight line, according to Newton's first law. If it is desired to apply Newton's laws in the rotating frame, it is necessary to introduce new, fictitious, forces to account for this curved motion. This is the centrifugal force. Consider a stone being whirled round on a string, in a horizontal plane. The only real force acting on the stone in the horizontal plane is the tension in the string. There are no other forces acting on the stone so there is a net force on the stone in the horizontal plane. In order to keep the stone moving in a circular path, this force, known as the centripetal force, must be continuously applied to the stone. As soon as it is removed the stone moves in a straight line. In a frame of reference rotating with the stone around the same axis as the stone, the stone is stationary.
Centrifugal force
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The interface of two immiscible liquids rotating around a vertical axis is an upward-opening circular paraboloid.
51.
Reactive centrifugal force
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In classical mechanics, a reactive centrifugal force forms part of an action–reaction pair with a centripetal force. In accordance with Newton's first law of motion, an object moves in a straight line in the absence of any external forces acting on the object. It is the reactive force, the subject of this article. Any force directed away from a center can be called "centrifugal". Centrifugal simply means "directed outward from the center". Similarly, centripetal means "directed toward the center". The figure at right shows a ball in circular motion held to its path by a massless string tied to an immovable post. The figure is an example of a real force. In this model, the string is assumed the rotational motion frictionless, so no propelling force is needed to keep the ball in circular motion. The string transmits the centrifugal force from the ball to the fixed post, pulling upon the post. Again according to the post exerts a reaction upon the string, labeled the post reaction, pulling upon the string. The two forces upon the string are opposite, exerting no net force upon the string, but placing the string under tension. It should be noted, however, that the reason the post appears to be "immovable" is because it is fixed to the earth. Even though the reactive centrifugal is rarely used in analyses in the literature, the concept is applied within some mechanical engineering concepts. An example of this kind of concept is an analysis of the stresses within a rapidly rotating turbine blade.
Reactive centrifugal force
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A two-shoe centrifugal clutch. The motor spins the input shaft that makes the shoes go around, and the outer drum (removed) turns the output power shaft.
52.
Coriolis force
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In physics, the Coriolis force is an inertial force that acts on objects that are in motion relative to a rotating reference frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise rotation, the force acts to the right. Early in the 20th century, the term Coriolis force began to be used in connection with meteorology. Deflection of an object due to the Coriolis force is called the'Coriolis effect'. Newton's laws of motion describe the motion of an object in an inertial frame of reference. When Newton's laws are transformed to a rotating frame of reference, the Coriolis force and centrifugal force appear. Both forces are proportional to the mass of the object. The Coriolis force is proportional to the rotation rate and the centrifugal force is proportional to its square. The centrifugal force acts outwards in the radial direction and is proportional to the distance of the body from the axis of the rotating frame. These additional forces are termed inertial forces, fictitious forces or pseudo forces. They allow the application of Newton's laws to a rotating system. They are correction factors that do not exist in a non-accelerating or inertial reference frame. A commonly encountered rotating reference frame is the Earth. The Coriolis effect is caused by the rotation of the Earth and the inertia of the mass experiencing the effect.
Coriolis force
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This low-pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.
Coriolis force
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Coordinate system at latitude φ with x -axis east, y -axis north and z -axis upward (that is, radially outward from center of sphere).
Coriolis force
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Cloud formations in a famous image of Earth from Apollo 17, makes similar circulation directly visible
Coriolis force
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A carousel is rotating counter-clockwise. Left panel: a ball is tossed by a thrower at 12:00 o'clock and travels in a straight line to the center of the carousel. While it travels, the thrower circles in a counter-clockwise direction. Right panel: The ball's motion as seen by the thrower, who now remains at 12:00 o'clock, because there is no rotation from their viewpoint.
53.
Pendulum (mathematics)
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The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle oscillations. The motion does not lose energy to resistance. The gravitational field is uniform. The support does not move. The differential equation given above is not easily solved, there is no solution that can be written in terms of elementary functions. However adding a restriction to the size of the oscillation's amplitude gives a form whose solution can be easily obtained. The error due to the approximation is of order θ3. The period of the motion, the time for a complete oscillation is, known as Christiaan Huygens's law for the period. Note that under the small-angle approximation, the period is independent of the amplitude θ0; this is the property of isochronism that Galileo discovered. T 0 = 2 π ℓ g can be expressed as ℓ = g π 2 T 0 2 4. If assuming the measurement is taking place on the Earth's surface, then g / π2 ≈ 1. The linear approximation gives s. Less than 0.2 %, is much less than that caused with geographical location. From here there are many ways to proceed to calculate the elliptic integral.
Pendulum (mathematics)
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Figure 1. Force diagram of a simple gravity pendulum.
Pendulum (mathematics)
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Animation of a pendulum showing the velocity and acceleration vectors.
54.
Angular displacement
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When dealing with the rotation of an object, it becomes simpler to consider the body itself rigid. In a realistic sense, all things can be deformable, however this impact is negligible. Thus the rotation of a rigid body over a fixed axis is referred to as rotational motion. In the example illustrated to the right, a particle on object P is at a fixed r from the origin, O, rotating counterclockwise. It becomes important to then represent the position of particle P in terms of its polar coordinates. In this particular example, the value of θ is changing, while the value of the radius remains the same. . If using radians, it provides a very simple relationship between distance traveled from the centre. Therefore 1 revolution is 2 π radians. Δ θ = θ − θ 1 which equals the Angular Displacement. In three dimensions, displacement is an entity with a direction and a magnitude. This entity is called an axis-angle. Despite having magnitude, angular displacement is not a vector because it does not obey the commutative law for addition. Nevertheless, in this case commutativity appears. Several ways to describe displacement exist, like rotation matrices or Euler angles.
Angular displacement
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Rotation of a rigid object P about a fixed object about a fixed axis O.
55.
Angular velocity
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This speed can be measured in terms of degrees per second, degrees per hour, etc.. Angular velocity is usually represented by the omega. The direction of the angular vector is perpendicular to the plane of rotation, in a direction, usually specified by the right-hand rule. The velocity of a particle is measured around or relative to a point, called the origin. If there is no radial component, then the particle moves in a circle. On the other hand, if there is no cross-radial component, then the particle moves along a straight line from the origin. Therefore, the angular velocity is completely determined by this component. The velocity in two dimensions is a pseudoscalar, a quantity that changes its sign under a parity inversion. The positive direction of rotation is taken, by convention, to be from the x axis. If the parity is inverted, but the orientation of a rotation is not, then the sign of the velocity changes. There are three types of velocity involved in the movement on an ellipse corresponding to the three anomalies. In three dimensions, the velocity becomes a bit more complicated. The velocity in this case is generally thought of as a vector, or more precisely, a pseudovector. It now has not only a direction as well. The direction describes the axis of rotation that Euler's rotation theorem guarantees must exist.
Angular velocity
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The angular velocity of the particle at P with respect to the origin O is determined by the perpendicular component of the velocity vector v.
56.
Galileo Galilei
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Galileo Galilei was an Italian polymath: astronomer, physicist, engineer, philosopher, mathematician, he played a major role in the scientific revolution of the seventeenth century. Galileo has been called the "father of the "father of science". Galileo also worked in applied science and technology, inventing an improved military compass and other instruments. Galileo's championing of heliocentrism and Copernicanism was controversial during his lifetime, when most subscribed to either geocentrism or the Tychonic system. He met with opposition from astronomers, who doubted heliocentrism because of the absence of an observed stellar parallax. He was tried by the Inquisition, found "vehemently suspect of heresy", forced to recant. He spent the rest of his life under house arrest. Three of Galileo's five siblings survived infancy. Michelangelo, also became a noted composer although he contributed during Galileo's young adulthood. Michelangelo would occasionally have to support his musical excursions. These financial burdens may have contributed to Galileo's early fire to develop inventions that would bring him additional income. When Galileo Galilei was eight, his family moved to Florence, but he was left with Jacopo Borghini for two years. Galileo then was educated at 35 southeast of Florence. The Italian male given name "Galileo" derives from the Latin "Galilaeus", meaning "of Galilee", a biblically significant region in Northern Israel. The biblical roots of Galileo's name and surname were to become the subject of a famous pun.
Galileo Galilei
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Portrait of Galileo Galilei by Giusto Sustermans
Galileo Galilei
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Galileo's beloved elder daughter, Virginia (Sister Maria Celeste), was particularly devoted to her father. She is buried with him in his tomb in the Basilica of Santa Croce, Florence.
Galileo Galilei
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Galileo Galilei. Portrait by Leoni
Galileo Galilei
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Cristiano Banti 's 1857 painting Galileo facing the Roman Inquisition
57.
Isaac Newton
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His book Philosophiæ Naturalis Principia Mathematica, first published in 1687, laid the foundations for classical mechanics. He shares credit with Gottfried Wilhelm Leibniz for the development of calculus. Newton's Principia formulated the laws of motion and universal gravitation, which dominated scientists' view of the physical universe for the next three centuries. This work also demonstrated that the motion of objects of celestial bodies could be described by the same principles. Newton formulated an empirical law of cooling, introduced the notion of a Newtonian fluid. He was the second Lucasian Professor of Mathematics at the University of Cambridge. In his later life, he became president of the Royal Society. He served the British government as Warden and Master of the Royal Mint. His father, also named Isaac Newton, had died three months before. Born prematurely, he was a small child; his mother Hannah Ayscough reportedly said that he could have fit inside a mug. Newton's mother had three children from her second marriage. Newton hated farming. Master at the King's School, persuaded his mother to send him back to school so that he might complete his education. Motivated partly by a desire for revenge against a schoolyard bully, Newton became the top-ranked student, distinguishing himself mainly by building models of windmills. In June 1661, Newton was admitted on the recommendation of his uncle Rev William Ayscough who had studied there.
Isaac Newton
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Portrait of Isaac Newton in 1689 (age 46) by Godfrey Kneller
Isaac Newton
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Newton in a 1702 portrait by Godfrey Kneller
Isaac Newton
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Isaac Newton (Bolton, Sarah K. Famous Men of Science. NY: Thomas Y. Crowell & Co., 1889)
Isaac Newton
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Replica of Newton's second Reflecting telescope that he presented to the Royal Society in 1672
58.
Johannes Kepler
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Johannes Kepler was a German mathematician, astronomer, astrologer. These works also provided one of the foundations for Isaac Newton's theory of universal gravitation. Kepler was a teacher at a seminary school in Graz, Austria, where he became an associate of Prince Hans Ulrich von Eggenberg. He was also an adviser to General Wallenstein. There was a strong division between astronomy and physics. Kepler was born on the feast day of St John the Evangelist, 1571, in the Free Imperial City of Weil der Stadt. Sebald Kepler, had been Lord Mayor of the city. By the time Johannes was born, the Kepler family fortune was in decline. He left the family when Johannes was five years old. He was believed to have died in the Eighty Years' War in the Netherlands. An innkeeper's daughter, was a healer and herbalist. Born prematurely, Johannes claimed to have been sickly as a child. Nevertheless, he often impressed travelers with his phenomenal mathematical faculty. He was developed a love for it that would span his entire life. At age six, he observed the Great Comet of 1577, writing that he "was taken to a high place to look at it."
Johannes Kepler
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A 1610 portrait of Johannes Kepler by an unknown artist
Johannes Kepler
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Birthplace of Johannes Kepler in Weil der Stadt
Johannes Kepler
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Portraits of Kepler and his wife in oval medallions
Johannes Kepler
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House of Johannes Kepler and Barbara Müller in Gössendorf near Graz (1597–1599)
59.
Jeremiah Horrocks
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Jeremiah Horrocks, sometimes given as Jeremiah Horrox, was an English astronomer. Jeremiah Horrocks was born at Lower Lodge Farm in a former royal deer park near Liverpool, Lancashire. His father James had moved to Toxteth Park to be subsequently married his master's daughter Mary. Both families were well educated Puritans; the Horrocks sent their younger sons to the University of Cambridge and the Aspinwalls favoured Oxford. In 1632 Horrocks matriculated as a sizar. At Cambridge he associated with the platonist John Worthington. In 1635 for reasons not clear Horrocks left Cambridge without graduating. Now committed to the study of astronomy, Horrocks began to collect astronomical books and equipment; by 1638 he owned the best telescope he could find. Liverpool was a seafaring town so navigational instruments such as the astrolabe and staff were easy to find. But there was no market for the specialised astronomical instruments he needed, so his only option was to make his own. He was well placed to do this; his father and uncles were watchmakers with expertise in creating precise instruments. According to local tradition in Much Hoole, he lived within the Bank Hall Estate, Bretherton. He posited that comets followed elliptical orbits. He anticipated Isaac Newton in suggesting the influence of the Sun well as the Earth on the moon's orbit. In the Principia Newton acknowledged Horrocks's work to his theory of lunar motion.
Jeremiah Horrocks
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Making the first observation of the transit of Venus in 1639
Jeremiah Horrocks
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A representation of Horrocks' recording of the transit published in 1662 by Johannes Hevelius
Jeremiah Horrocks
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The title page of Jeremiah Horrocks' Opera Posthuma, published by the Royal Society in 1672.
Jeremiah Horrocks
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Jeremiah Horrocks Observatory on Moor Park, Preston
60.
Edmond Halley
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Edmond Halley, FRS was an English astronomer, geophysicist, mathematician, meteorologist, physicist, best known for computing the orbit of Halley's Comet. Halley was the second Astronomer Royal in Britain, succeeding John Flamsteed. He was born in east London. Edmond Halley Sr. came from a Derbyshire family and was a wealthy soap-maker in London. As a child, he was very interested in mathematics. Halley studied at The Queen's College, Oxford. While still an undergraduate, he published papers on sunspots. Halley returned in May 1678. In the following year Halley went on behalf of the Royal Society to help resolve a dispute. Because astronomer Johannes Hevelius did not use a telescope, his observations had been questioned by Robert Hooke. He observed and verified the quality of Hevelius' observations. In 1679 he published the results from his observations as Catalogus Stellarum Australium which included details of 341 southern stars. These additions to contemporary star maps earned comparison with Tycho Brahe: e.g. "the southern Tycho" as described by Flamsteed. He was elected as a Fellow of the Royal Society at the age of 22. In 1686, he published the second part of the results from his Helenian expedition, being a chart on trade winds and monsoons.
Edmond Halley
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Bust of Halley (Royal Observatory, Greenwich)
Edmond Halley
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Portrait by Thomas Murray, c. 1687
Edmond Halley
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Halley's grave
Edmond Halley
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Plaque in South Cloister of Westminster Abbey
61.
Leonhard Euler
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He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function. Euler is also known for his work in mechanics, music theory. Euler was one of the most eminent mathematicians of the 18th century, is held to be one of the greatest in history. He is also widely considered to be the most prolific mathematician of all time. His collected works fill 60 to 80 quarto volumes, more than anybody in the field. He spent most of his adult life in St. Petersburg, Russia, in Berlin, then the capital of Prussia. A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is the master of us all." He had two younger sisters: Anna Maria and Maria Magdalena, a younger brother Johann Heinrich. Soon after the birth of Leonhard, the Eulers moved from Basel to the town of Riehen, where Euler spent most of his childhood. Euler's formal education started in Basel, where he was sent to live with his maternal grandmother. During that time, he was receiving Saturday afternoon lessons from Johann Bernoulli, who quickly discovered his new pupil's incredible talent for mathematics. In 1726, Euler completed a dissertation on the propagation of sound with the title De Sono. At that time, he was unsuccessfully attempting to obtain a position at the University of Basel. Pierre Bouguer, who became known as "the father of naval architecture", won and Euler took second place. Euler later won this annual prize twelve times.
Leonhard Euler
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Portrait by Jakob Emanuel Handmann (1756)
Leonhard Euler
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1957 Soviet Union stamp commemorating the 250th birthday of Euler. The text says: 250 years from the birth of the great mathematician, academician Leonhard Euler.
Leonhard Euler
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Stamp of the former German Democratic Republic honoring Euler on the 200th anniversary of his death. Across the centre it shows his polyhedral formula, nowadays written as " v − e + f = 2".
Leonhard Euler
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Euler's grave at the Alexander Nevsky Monastery
62.
Jean le Rond d'Alembert
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Jean-Baptiste le Rond d'Alembert was a French mathematician, mechanician, physicist, philosopher, music theorist. Until 1759 he was also co-editor with Denis Diderot of the Encyclopédie. D'Alembert's formula for obtaining solutions to the wave equation is named after him. The wave equation is sometimes referred to as d'Alembert's equation. Born in Paris, d'Alembert was the natural son of an artillery officer. Destouches was abroad at the time of d'Alembert's birth. Days after birth his mother left him on the steps of the Saint-Jean-le-Rond de Paris church. According to custom, he was named after the patron saint of the church. Destouches secretly paid for the education of Jean le Rond, but did not want his paternity officially recognized. D'Alembert first attended a private school. The chevalier Destouches left d'Alembert an annuity of 1200 livres on his death in 1726. Under the influence of the Destouches family, at the age of twelve d'Alembert entered the Jansenist Collège des Quatre-Nations. Here he studied the arts, graduating as baccalauréat en arts in 1735. In his later life, D'Alembert scorned the Cartesian principles he had been taught by the Jansenists: the vortices". The Jansenists steered D'Alembert toward an ecclesiastical career, attempting to deter him from pursuits such as poetry and mathematics.
Jean le Rond d'Alembert
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Jean-Baptiste le Rond d'Alembert, pastel by Maurice Quentin de La Tour
63.
Alexis Clairaut
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Alexis Claude Clairaut was a French mathematician, astronomer, geophysicist. Clairaut was one of the key figures in the expedition to Lapland that helped to confirm Newton's theory for the figure of the Earth. In that context, Clairaut worked out a mathematical result now known as "Clairaut's theorem". He also tackled the gravitational three-body problem, being the first to obtain a satisfactory result for the apsidal precession of the Moon's orbit. In mathematics he is also credited with Clairaut's equation and Clairaut's relation. He was born to Catherine Petit Clairaut. The couple had 20 children, however only a few of them survived childbirth. His father taught mathematics. Alexis was a prodigy — at the age of ten he began studying calculus. He known for leading an social life. Though he led a fulfilling social life, he was very prominent in the advancement of learning in young mathematicians. He was elected a Fellow of the Royal Society of London in November, 1737. Clairaut died in Paris in 1765. They sought to prove if Newton's theory and calculations were correct or not. Before the expedition team returned to Paris, Clairaut sent his calculations to the Royal Society of London.
Alexis Clairaut
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Alexis Claude Clairaut
64.
Joseph-Louis Lagrange
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Joseph-Louis Lagrange, born Giuseppe Lodovico Lagrangia or Giuseppe Ludovico De la Grange Tournier, was an Italian Enlightenment Era mathematician and astronomer. Lagrange made significant contributions to the fields of both celestial mechanics. In 1787, at age 51, he moved from Berlin to Paris and became a member of the French Academy. He remained in France until the end of his life. Lagrange was one of the creators of the calculus of variations, deriving the Euler–Lagrange equations for extrema of functionals. He also extended the method to take into account possible constraints, arriving at the method of Lagrange multipliers. He proved that every natural number is a sum of four squares. His treatise Theorie des fonctions analytiques laid some of the foundations of group theory, anticipating Galois. In calculus, Lagrange developed a novel approach to interpolation and Taylor series. Born as Giuseppe Lodovico Lagrangia, Lagrange was of Italian and French descent. His mother was from the countryside of Turin. He was raised as a Roman Catholic. A career as a lawyer was planned out for Lagrange by his father, certainly Lagrange seems to have accepted this willingly. He studied at the University of Turin and his favourite subject was classical Latin. At first he had no great enthusiasm for mathematics, finding Greek geometry rather dull.
Joseph-Louis Lagrange
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Joseph-Louis (Giuseppe Luigi), comte de Lagrange
Joseph-Louis Lagrange
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Lagrange's tomb in the crypt of the Panthéon
65.
Pierre-Simon Laplace
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Pierre-Simon, marquis de Laplace was an influential French scholar whose work was important to the development of mathematics, statistics, physics and astronomy. He summarized and extended the work of his predecessors in his five-volume Mécanique Céleste. This work translated the geometric study of classical mechanics to one based on calculus, opening up a broader range of problems. In statistics, the Bayesian interpretation of probability was developed mainly by Laplace. The Laplacian differential operator, widely used in mathematics, is also named after him. Laplace is remembered as one of the greatest scientists of all time. Laplace was named a marquis after the Restoration. Laplace was born in Beaumont-en-Auge, Normandy on 23 March 1749 at Beaumont-en-Auge, a village four miles west of Pont l'Eveque in Normandy. According to W. W. Rouse Ball, His father, Pierre de Laplace, owned and farmed the small estates of Maarquis. His great-uncle, Maitre Oliver de Laplace, had held the title of Chirurgien Royal. It was here that Laplace was educated and was provisionally a professor. It was here he wrote his first paper published in the Mélanges of the Royal Society of Turin, Tome iv. 1766–1769, at least two years before he went at 22 or 23 to Paris in 1771. Thus before he was 20 he was in touch with Lagrange in Turin. He did not go to Paris a self-taught lad with only a background!
Pierre-Simon Laplace
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Pierre-Simon Laplace (1749–1827). Posthumous portrait by Jean-Baptiste Paulin Guérin, 1838.
Pierre-Simon Laplace
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Laplace's house at Arcueil.
Pierre-Simon Laplace
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Laplace.
Pierre-Simon Laplace
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Tomb of Pierre-Simon Laplace
66.
William Rowan Hamilton
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Sir William Rowan Hamilton PRIA FRSE was an Irish physicist, astronomer, mathematician, who made important contributions to classical mechanics, optics, algebra. His studies of optical systems led him to discover new mathematical concepts and techniques. His best known contribution to mathematical physics is the reformulation of Newtonian mechanics, now called Hamiltonian mechanics. This work has proven central to the development of quantum mechanics. In pure mathematics, Hamilton is best known as the inventor of quaternions. He is said to have shown immense talent at a very early age. Astronomer Bishop Dr. John Brinkley remarked of the 18-year-old Hamilton, ` This young man, I do not say is, the first mathematician of his age.' He also invented "icosian calculus", which he used to investigate closed edge paths on a dodecahedron that visit each vertex once. He was the fourth of nine children born to Archibald Hamilton, who lived in Dublin at 38 Dominick Street. Hamilton's father, from Dunboyne, worked as a solicitor. Meath. His uncle soon discovered that Hamilton had a remarkable ability to learn languages, from a young age, had displayed an uncanny ability to acquire them. These included Persian, Arabic, Hindustani, Sanskrit, even Marathi and Malay. In September 1813 the American calculating prodigy Zerah Colburn was being exhibited in Dublin. Colburn was 9, a year older than Hamilton.
William Rowan Hamilton
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Quaternion Plaque on Broom Bridge
William Rowan Hamilton
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William Rowan Hamilton (1805–1865)
William Rowan Hamilton
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Irish commemorative coin celebrating the 200th Anniversary of his birth.
67.
Daniel Bernoulli
–
Daniel Bernoulli FRS was a Swiss mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family. He is particularly remembered for his applications of mathematics for his pioneering work in probability and statistics. Daniel Bernoulli was born in Groningen, into a family of distinguished mathematicians. The Bernoulli family emigrated to escape the Spanish persecution of the Huguenots. After a brief period in Frankfurt the family moved in Switzerland. Daniel was the son of nephew of Jacob Bernoulli. He had two brothers, Johann II. Daniel Bernoulli was described by W. W. Rouse Ball as "by far the ablest of the younger Bernoullis". He is said to have had a bad relationship with his father. Johann Bernoulli also plagiarized some key ideas in his own book Hydraulica which he backdated to before Hydrodynamica. Despite Daniel's attempts at reconciliation, his father carried the grudge until his death. Around age, his father, Johann, encouraged him to study business, there being poor rewards awaiting a mathematician. However, Daniel refused, because he wanted to study mathematics. He later studied business. Daniel earned a PhD in anatomy and botany in 1721.
Daniel Bernoulli
–
Daniel Bernoulli
68.
Johann Bernoulli
–
Johann Bernoulli was a Swiss mathematician and was one of the many prominent mathematicians in the Bernoulli family. He is educating Leonhard Euler in the pupil's youth. Johann began studying medicine at Basel University. However, Johann Bernoulli began studying mathematics on the side with his older brother Jacob. Throughout Johann Bernoulli’s education at Basel University the Bernoulli brothers worked together spending much of their time studying the newly discovered infinitesimal calculus. They were among the first mathematicians to apply it to various problems. After graduating from Basel University Johann Bernoulli moved to teach differential equations. Later, in 1694, he married Dorothea Falkner and soon after accepted a position at the University of Groningen. At the request of Johann Bernoulli's father-in-law, Johann Bernoulli began the voyage back in 1705. Just after setting out on the journey he learned to tuberculosis. As a student of Leibniz's calculus, Johann Bernoulli sided with him in the Newton -- Leibniz debate over who deserved credit for the discovery of calculus. Johann Bernoulli defended Leibniz by showing that he had solved certain problems with his methods that Newton had failed to solve. Johann Bernoulli also promoted Descartes' theory over Newton's theory of gravitation. This ultimately delayed acceptance of Newton’s theory in continental Europe. In consequence he was disqualified for the prize, won by Maclaurin.
Johann Bernoulli
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Johann Bernoulli (portrait by Johann Rudolf Huber, circa 1740)
69.
Augustin-Louis Cauchy
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Baron Augustin-Louis Cauchy FRS FRSE was a French mathematician reputed as a pioneer of analysis. Cauchy was one of the first to prove theorems of calculus rigorously, rejecting the heuristic principle of the generality of algebra of earlier authors. Cauchy singlehandedly founded complex analysis and the study of permutation groups in abstract algebra. Cauchy had a great influence over his contemporaries and successors. His writings range widely in mathematical physics. "More theorems have been named for Cauchy than for any other mathematician." Cauchy was a prolific writer; he wrote five complete textbooks. He was the son of Louis François Cauchy and Marie-Madeleine Desestre. He married Aloise de Bure in 1818. She was a close relative of the publisher who published most of Cauchy's works. By her Cauchy had two daughters, Marie Mathilde. Cauchy's father was a high official in the Parisian Police of the New Régime. Cauchy lost his position because of the French Revolution that broke out month before Augustin-Louis was born. The Cauchy family survived the following Reign of Terror by escaping to Arcueil, where Cauchy received his first education, from his father. After the execution of Robespierre, it was safe for the family to return to Paris.
Augustin-Louis Cauchy
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Cauchy around 1840. Lithography by Zéphirin Belliard after a painting by Jean Roller.
Augustin-Louis Cauchy
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The title page of a textbook by Cauchy.
Augustin-Louis Cauchy
–
Leçons sur le calcul différentiel, 1829
70.
Physics
–
One of the main goal of physics is to understand how the universe behaves. Physics is one of perhaps the oldest through its inclusion of astronomy. The boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences while opening new avenues of research in areas such as philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. The United Nations named the World Year of Physics. Astronomy is the oldest of the natural sciences. The planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, these early observations laid the foundation for later astronomy. In the book, he was also the first to delved further into the way the eye itself works. Fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haytham's Optics ranks alongside that of Newton's work of the same title, published 700 years later. The translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the same devices as what Ibn Al Haytham understand the way light works. From this, important things as eyeglasses, magnifying glasses, telescopes, cameras were developed.
Physics
–
Further information: Outline of physics
Physics
–
Ancient Egyptian astronomy is evident in monuments like the ceiling of Senemut's tomb from the Eighteenth Dynasty of Egypt.
Physics
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Sir Isaac Newton (1643–1727), whose laws of motion and universal gravitation were major milestones in classical physics
Physics
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Albert Einstein (1879–1955), whose work on the photoelectric effect and the theory of relativity led to a revolution in 20th century physics
71.
Measure (mathematics)
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In this sense, a measure is a generalization of the concepts of length, volume. For instance, the Lebesgue measure of the interval in the real numbers is its length in the everyday sense of the word – specifically, 1. A measure is a function that assigns a non-negative real number or + ∞ to subsets of a set X. This problem was resolved by defining measure only on a sub-collection of all subsets; the measurable subsets, which are required to form a σ-algebra. This means that countable intersections and complements of measurable subsets are measurable. Indeed, their existence is a non-trivial consequence of the axiom of choice. The main applications of measures are in the foundations of the Lebesgue integral, in ergodic theory. Ergodic theory considers measures that are invariant under, or arise naturally from, a dynamical system. Let X be a set and Σ a σ-algebra over X. Null empty set: μ = 0. The pair is called a measurable space, the members of Σ are called measurable sets. A triple is called a space. A measure is a measure with total measure one -- i.e. μ = 1. μ = 1. A space is a measure space with a probability measure.
Measure (mathematics)
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Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0.
72.
Net force
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In physics, net force is the overall force acting on an object. It is possible for a system of forces to define a torque-free force. It is not always possible to find a torque-free force. The sum of forces acting on a particle is called the net force. The net force is a single force that replaces the effect of the original forces on the particle's motion. It gives the same acceleration as all those actual forces together as described by the Newton's second law of motion. Graphically, a force is represented to a point B which defines its direction and magnitude. The length of the segment AB represents the magnitude of the force. Vector calculus was developed in the late early 1900s. The rule used for the addition of forces, however, dates from antiquity and is noted explicitly by Galileo and Newton. The diagram shows the addition of F → 2. The sum → of the two forces is drawn as the diagonal of a parallelogram defined by the two forces. Forces applied to an extended body can have different points of application. Forces are bound can be added only if they are applied at the same point. The net force on a body applied at a single point with the appropriate torque is known as torque.
Net force
–
A diagrammatic method for the addition of forces.
Net force
–
How a force accelerates a body.
Net force
–
Graphical placing of the resultant force.
73.
Gravitation
–
Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since energy and mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. On Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has an infinite range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape once past its event horizon, not even light. More gravity results in gravitational time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature. As a consequence, gravity has a negligible influence on the behavior of subatomic particles, plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the dominant interaction at the macroscopic scale, is the cause of the formation, shape and trajectory of astronomical bodies. While the modern European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Later, the works of Brahmagupta referred to the presence of this force. Modern work on gravitational theory began with the work of Galileo Galilei in the late 16th and early 17th centuries. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
Gravitation
–
Sir Isaac Newton, an English physicist who lived from 1642 to 1727
Gravitation
–
Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.
Gravitation
–
Ball falling freely under gravity. See text for description.
Gravitation
–
Gravity acts on stars that conform our Milky Way.
74.
SI unit
–
The International System of Units is the modern form of the metric system, is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units. The system was published as the result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units rather than any variant of the centimetre-gram-second system. The International System of Units has been adopted by most developed countries; however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the kilogram as standards of length and mass respectively. In the 1830s Carl Friedrich Gauss laid the foundations based on length, mass, time. Meanwhile, in 1875, the Treaty of the Metre passed responsibility for verification of the kilogram and metre against agreed prototypes to international control. In 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, ampere, candela. In 1971, amount of substance represented by the mole, was added to the definition of SI. On 11 the committee proposed the names metre, are, litre and grave for the units of length, area, capacity, mass, respectively. On December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the earth’s magnetic field had only been described in relative terms. The resultant calculations enabled him to assign dimensions based to the magnetic field.
SI unit
–
Stone marking the Austro-Hungarian /Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated).
SI unit
–
The seven base units in the International System of Units
SI unit
–
Carl Friedrich Gauss
SI unit
–
Thomson
75.
Kilogram
–
1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The kilogram is the only SI unit with an SI prefix as part of its name. 17 derived units in the SI system are defined relative to the kilogram, so its stability is important. Only 8 other units do not require the kilogram in their definition: temperature, frequency, length, angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting. There are currently different proposals for the redefinition; these are described in the Proposed Future Definitions section below. The International Prototype Kilogram is rarely handled. In the decree of 1795, the gramme thus replaced gravet, kilogramme replaced grave. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common. UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. The kilogram is a unit of a property which corresponds to the common perception of how "heavy" an object is. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the floor; they are "weightless". The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. Accordingly, a provisional standard was made as a single-piece, metallic artifact one thousand times as massive as the gram -- the kilogram.
Kilogram
–
A domestic-quality one-kilogram weight made of cast iron (the credit card is for scale). The shape follows OIML recommendation R52 for cast-iron hexagonal weights
Kilogram
–
Measurement of weight – gravitational attraction of the measurand causes a distortion of the spring
Kilogram
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Measurement of mass – the gravitational force on the measurand is balanced against the gravitational force on the weights.
Kilogram
–
The Arago kilogram, an exact copy of the "Kilogramme des Archives" commissioned in 1821 by the US under supervision of French physicist François Arago that served as the US's first kilogram standard of mass until 1889, when the US converted to primary metric standards and received its current kilogram prototypes, K4 and K20.
76.
Weight
–
In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. The unit of measurement for weight is that of force, which in the International System of Units is the newton. In this sense of weight, a body can be weightless only if it is away from any other mass. Although mass are scientifically distinct quantities, the terms are often confused with each other in everyday use. There is also a rival tradition within Newtonian engineering which sees weight as that, measured when one uses scales. There the weight is a measure of the magnitude of the force exerted on a body. Thus, in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless. The famous apple falling from the tree, on its way to meet the ground near Isaac Newton, is weightless. In the community, a considerable debate has existed for over half a century on how to define weight for their students. The current situation is that a multiple set of concepts find use in their various contexts. Discussion of the concepts of lightness date back to the ancient Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire and water.
Weight
–
Ancient Greek official bronze weights dating from around the 6th century BC, exhibited in the Ancient Agora Museum in Athens, housed in the Stoa of Attalus.
Weight
–
Weighing grain, from the Babur-namah
Weight
–
This top-fuel dragster can accelerate from zero to 160 kilometres per hour (99 mph) in 0.86 seconds. This is a horizontal acceleration of 5.3 g. Combined with the vertical g-force in the stationary case the Pythagorean theorem yields a g-force of 5.4 g. It is this g-force that causes the driver's weight if one uses the operational definition. If one uses the gravitational definition, the driver's weight is unchanged by the motion of the car.
Weight
–
Measuring weight versus mass
77.
Weighing scale
–
Weighing scales are devices to measure weight or calculate mass. Scales and balances are widely used in commerce, as many products are sold and packaged by weight. Very accurate balances, called analytical balances are used in scientific fields such as chemistry. By the 1940s various electronic devices were being attached to these designs to make readings more accurate. A spring scale measures weight by reporting the distance that a spring deflects under a load. Spring scales measure force, the tension force of constraint acting on an object, opposing the local force of gravity. They are usually calibrated so that measured force translates to mass at earth's gravity. The object to be weighed can be set on a platform. In a spring scale, the spring either stretches or compresses. By Hooke's law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Pinion mechanisms are often used to convert the linear motion to a reading. With proper manufacturing and setup, however, spring scales can be rated as legal for commerce. To remove the error, a commerce-legal scale must either be used at a fairly constant temperature. To eliminate the effect of gravity variations, a commerce-legal spring scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use hydraulic force to sense weight.
Weighing scale
–
Digital kitchen scale, a strain gauge scale
Weighing scale
–
Scales used for trade purposes in the state of Florida, as this scale at the checkout in a cafeteria, are inspected for accuracy by the FDACS's Bureau of Weights and Measures.
Weighing scale
–
A two-pan balance
Weighing scale
–
Two 10- decagram masses
78.
Newtonian physics
–
In physics, classical mechanics is one of the two major sub-fields of mechanics, along with quantum mechanics. Classical mechanics is concerned with the set of physical laws describing the motion of bodies under the influence of a system of forces. The study of the motion of bodies is an ancient one, making classical mechanics one of the largest subjects in science, engineering and technology. It is also widely known as Newtonian mechanics. Classical mechanics describes the motion of macroscopic objects, from projectiles to parts of machinery, well as astronomical objects, such as spacecraft, planets, stars, galaxies. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases and other specific sub-topics. When classical mechanics can not apply, such as at the quantum level with high speeds, quantum field theory becomes applicable. Since these aspects of physics were developed long before the emergence of quantum relativity, some sources exclude Einstein's theory of relativity from this category. However, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most accurate form. Later, more general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and Hamiltonian mechanics. They extend substantially beyond Newton's work, particularly through their use of analytical mechanics. The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as point particles. The motion of a particle is characterized by a small number of parameters: its position, mass, the forces applied to it. Each of these parameters is discussed in turn.
Newtonian physics
–
Sir Isaac Newton (1643–1727), an influential figure in the history of physics and whose three laws of motion form the basis of classical mechanics
Newtonian physics
–
Diagram of orbital motion of a satellite around the earth, showing perpendicular velocity and acceleration (force) vectors.
Newtonian physics
–
Hamilton 's greatest contribution is perhaps the reformulation of Newtonian mechanics, now called Hamiltonian mechanics.
79.
Special relativity
–
In physics, special relativity is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates: The laws of physics are invariant in all inertial systems. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source. It was originally proposed in 1905 by Albert Einstein in the paper "On the Electrodynamics of Moving Bodies". As of today, special relativity is the most accurate model of motion at any speed. Even so, the Newtonian mechanics model is still useful as an approximation at small velocities relative to the speed of light. It has replaced the conventional notion of an universal time with the notion of a time, dependent on spatial position. Rather than an invariant interval between two events, there is an invariant interval. A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations. Time and space cannot be defined separately from each other. Rather space and time are interwoven into a single continuum known as spacetime. Events that occur at the same time for one observer can occur at different times for another. The theory is "special" in that it only applies in the special case where the curvature of spacetime due to gravity is negligible. In order to include gravity, Einstein formulated general relativity in 1915. Special relativity, contrary to some outdated descriptions, is capable of handling accelerated frames of reference.
Special relativity
–
Albert Einstein around 1905, the year his " Annus Mirabilis papers " – which included Zur Elektrodynamik bewegter Körper, the paper founding special relativity – were published.
80.
Forms of energy
–
In the context of physical science, several forms of energy have been identified. These include: Some entries in the above list comprise others in the list. The list is not necessarily complete. Whenever physical scientists discover that a certain phenomenon appears to violate the law of conservation, new forms are typically added that account for the discrepancy. Work are special cases in that they are not properties of systems, but are instead properties of processes that transfer energy. Work are measured as positive or negative depending on which side of the transfer we view them from. These include gravitational energy, several types of nuclear energy, magnetic energy. Familiar types of energy are a varying mix of both potential and kinetic energy. An example is mechanical energy, the sum in a system. For example, one can speak of macroscopic kinetic energy, which do not include thermal potential and kinetic energy. Similar remarks apply to nuclear most other forms of energy. Energy may be transformed at various efficiencies. Items that transform between these forms are called transducers. General non-relativistic mechanics energy manifest in many forms, but can be broadly classified into potential energy and kinetic energy. The term potential energy is a very general term, because it exists in all force fields, such as gravitation, magnetic fields.
Forms of energy
–
Thermal energy is energy of microscopic constituents of matter, which may include both kinetic and potential energy.
Forms of energy
81.
Gravitational force
–
Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since mass are equivalent, all forms including light, also cause gravitation and are under the influence of it. On Earth, gravity gives weight to physical objects and causes the ocean tides. Gravity has an infinite range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape once past its event horizon, not even light. More gravity results in gravitational time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature. As a consequence, gravity has a negligible influence on the behavior of subatomic particles, plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the cause of the formation, trajectory of astronomical bodies. While the modern European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Later, the works of Brahmagupta referred to the presence of this force. Modern work on gravitational theory began in the late 16th and 17th centuries. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated air resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
Gravitational force
–
Sir Isaac Newton, an English physicist who lived from 1642 to 1727
Gravitational force
–
Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.
Gravitational force
–
Ball falling freely under gravity. See text for description.
Gravitational force
–
Gravity acts on stars that conform our Milky Way.
82.
Newton's second law of motion
–
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between its motion in response to those forces. They have been expressed in several different ways, over nearly three centuries, can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to investigate the motion of systems. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of any structure. Newton's laws hold only to a certain set of frames of reference called inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given mass, acceleration, force are assumed to be externally defined quantities. Not the only interpretation of the one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F = 0 ⇔ d v d t = 0.
Newton's second law of motion
–
Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's second law of motion
–
Isaac Newton (1643–1727), the physicist who formulated the laws
83.
Gravitational constant
–
Its value is approximately 6989667400000000000♠6.674×10−11 N⋅m2/kg2. G, is the gravitational constant. Colloquially, the gravitational constant is also called "Big G", for disambiguation with "small g", the gravitational field of Earth. The two quantities are related by g = G M r E − 2. The gravitational constant is a constant, difficult to measure with high accuracy. This is because the gravitational force is extremely weak compared with fundamental forces. In cgs, G can be written as: G ≈ 6.674 × 10 − 8 m 3 g − 1 s − 2. In Planck units, G has the numerical value of 7000100000000000000 ♠ 1. In astrophysics, it is convenient to measure distances in parsecs, velocities in kilometers per second and masses in solar units M⊙. In these units, the gravitational constant is: G ≈ 4.302 × − 3 p c M ⊙ − 1 2. It follows that P 2 = 3 π G V M ≈ 10.896 h r 2 g c m − 3 V M. This way of expressing G shows the relationship between the period of a satellite orbiting just above its surface. Cavendish measured G implicitly, using a balance invented by the geologist Rev. John Michell. He used a horizontal beam with lead balls whose inertia he could tell by timing the beam's oscillation. Their faint attraction to other balls placed alongside the beam was detectable by the deflection it caused.
Gravitational constant
–
The gravitational constant G is a key quantity in Newton's law of universal gravitation.
84.
Equivalence principle
–
For Newton's equation of motion in a gravitational field, written out in full, it is: ⋅ = ⋅. It is only when there is numerical equality between the gravitational mass that the acceleration is independent of the nature of the body. This can be deduced without knowing in what manner gravity decreases with distance, but requires assuming the equivalency between gravity and inertia. The 1/54 ratio is Kepler's estimate of the Moon -- Earth ratio, based on their diameters. The accuracy of his statement can be deduced by using Galileo's gravitational observation that distance D = a t 2. Setting these accelerations equal for a mass is the equivalence principle. Einstein stated it thus: we assume a corresponding acceleration of the reference system. That is, being on the surface of the Earth is equivalent to being inside a spaceship, being accelerated by its engines. From this principle, Einstein deduced that free-fall is actually inertial motion. Objects in free-fall do not experience being accelerated downward but rather no acceleration. In an inertial frame of reference bodies obey Newton's first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the line of an inertial particle or pulse of light is as straight as possible. Such a line is called a geodesic and from the point of view of the inertial frame is a straight line. This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any. This is possible because space is radically curved to a large gravitational mass.
Equivalence principle
–
General relativity
85.
General relativity
–
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. In particular, the curvature of spacetime is directly related to the momentum of whatever matter and radiation are present. The relation is specified by a system of partial differential equations. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational time delay. The predictions of general relativity have been confirmed to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. Einstein's theory has astrophysical implications. General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics LIGO. In addition, general relativity is the basis of cosmological models of a consistently expanding universe. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his relativistic framework. The Einstein field equations are very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. The objects known today as black holes. In 1917, Einstein applied his theory as a whole initiating the field of relativistic cosmology.
General relativity
–
A simulated black hole of 10 solar masses within the Milky Way, seen from a distance of 600 kilometers.
General relativity
–
Albert Einstein developed the theories of special and general relativity. Picture from 1921.
General relativity
–
Einstein cross: four images of the same astronomical object, produced by a gravitational lens
General relativity
–
Artist's impression of the space-borne gravitational wave detector LISA
86.
Orders of magnitude (mass)
–
To help compare different orders of magnitude, the following lists describe various mass levels between 10−40 kg and 1053 kg. The table below is based in the International System of Units. The kilogram is the standard unit to include an SI prefix as part of its name. The gram is an SI derived unit of mass. However, the names of all SI mass units are based on gram, rather than on kilogram; thus 103 kg is a megagram, not a "kilokilogram". The tonne is a SI-compatible unit of mass equal to a megagram, or 103 kg. The unit is often used with SI prefixes. Other units of mass are also in use. Historical units include the stone, the pound, the grain. For subatomic particles, physicists use the mass equivalent to the energy represented by an electronvolt. At the atomic level, chemists use the mass of one-twelfth of a carbon-12 atom. Astronomers use the mass of the sun. Planck's law allows for the existence of photons with arbitrarily low energies. This series on orders of magnitude does not have a range of larger masses Mass units conversion calculator Mass units conversion calculator JavaScript
Orders of magnitude (mass)
–
Iron weights up to 50 kilograms depicted in Dictionnaire encyclopédique de l'épicerie et des industries annexes.
87.
SI base units
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The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. Many other units, such as the litre, are formally not part of the SI, but are accepted for use with SI. The definitions of the base units have been modified several times since the Metre Convention in 1875, new additions of base units have occurred. However, the candela are linked to the mass of the platinum -- iridium cylinder stored in a vault near Paris. Two possibilities have attracted particular attention: the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011.
SI base units
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The seven SI base units and the interdependency of their definitions: for example, to extract the definition of the metre from the speed of light, the definition of the second must be known while the ampere and candela are both dependent on the definition of energy which in turn is defined in terms of length, mass and time.
88.
International System of Units
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The International System of Units is the modern form of the metric system, is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units. The system was published in 1960 as the result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units rather than any variant of the centimetre-gram-second system. The International System of Units has been adopted by most developed countries; however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the kilogram as standards of mass respectively. In the 1830s Carl Friedrich Gauss laid the foundations based on length, time. Meanwhile, in 1875, the Treaty of the Metre passed responsibility to international control. In 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, candela. In 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 the committee are, litre and grave for the units of length, area, capacity, mass, respectively. On 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the earth’s magnetic field had only been described in relative terms. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field.
International System of Units
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Stone marking the Austro-Hungarian /Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated).
International System of Units
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The seven base units in the International System of Units
International System of Units
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Carl Friedrich Gauss
International System of Units
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Thomson
89.
Melting point
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The melting point of a solid is the temperature at which it changes state from solid to liquid at atmospheric pressure. At the melting point the liquid phase exist in equilibrium. The melting point of a substance is usually specified at standard pressure. When considered as the temperature of the reverse change to solid, it is referred to as the freezing point or crystallization point. Because of the ability of some substances to supercool, the point is not considered as a characteristic property of a substance. For most substances, freezing points are approximately equal. For example, the melting point and point of mercury is 234.32 kelvins. However, certain substances possess differing solid-liquid transition temperatures. For example, agar melts from 31 ° C to 40 ° C; such direction dependence is known as hysteresis. The melting point of ice at 1 atmosphere of pressure is very close to 0 ° C; this is also known as the point. The chemical element with the highest point is tungsten, at 3687 K; this property makes tungsten excellent for use as filaments in light bulbs. Tantalum carbide is a refractory compound with a very high melting point of 4215 K. Many laboratory techniques exist for the determination of melting points. A Kofler bench is a strip with a temperature gradient. Any substance can be placed on a section of the strip revealing its thermal behaviour at the temperature at that point.
Melting point
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Melting points (in blue) and boiling points (in pink) of the first eight carboxylic acids (°C)
Melting point
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Kofler bench with samples for calibration
Melting point
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Automatic digital melting point meter
Melting point
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Pressure dependence of water melting point
90.
International prototype kilogram
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1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The kilogram is the only SI unit with an SI prefix as part of its name. 17 derived units in the SI system are defined relative to the kilogram, so its stability is important. Only 8 other units do not require the kilogram in their definition: temperature, frequency, length, angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting. There are currently different proposals for the redefinition; these are described in the Proposed Future Definitions section below. The International Prototype Kilogram is rarely handled. In the decree of 1795, the gramme thus replaced gravet, kilogramme replaced grave. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common. UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. The kilogram is a unit of a property which corresponds to the common perception of how "heavy" an object is. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the floor; they are "weightless". The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. Accordingly, a provisional standard was made as a single-piece, metallic artifact one thousand times as massive as the gram -- the kilogram.
International prototype kilogram
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A domestic-quality one-kilogram weight made of cast iron (the credit card is for scale). The shape follows OIML recommendation R52 for cast-iron hexagonal weights
International prototype kilogram
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Measurement of weight – gravitational attraction of the measurand causes a distortion of the spring
International prototype kilogram
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Measurement of mass – the gravitational force on the measurand is balanced against the gravitational force on the weights.
International prototype kilogram
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The Arago kilogram, an exact copy of the "Kilogramme des Archives" commissioned in 1821 by the US under supervision of French physicist François Arago that served as the US's first kilogram standard of mass until 1889, when the US converted to primary metric standards and received its current kilogram prototypes, K4 and K20.
91.
Planck constant
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The Planck constant is a physical constant, the quantum of action, central in quantum mechanics. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called the photon. This leads to another relationship involving the Planck constant. With p denoting the linear momentum of a particle, the de Broglie wavelength λ of the particle is given by λ = h p. In applications where it is natural to use the angular frequency it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, is denoted ħ: ℏ = h 2 π. This was confirmed by experiments soon afterwards. This holds throughout quantum theory, including electrodynamics. These two relations are the temporal and spatial component parts of the special relativistic expression using 4-Vectors. P μ = = ℏ K μ = ℏ Classical statistical mechanics requires the existence of h. Eventually, following upon Planck's discovery, it was recognized that physical action cannot take on an arbitrary value. Instead, it must be some multiple of a very small quantity, the "quantum of action", now called the Planck constant. Thus there is no value of the action as classically defined.
Planck constant
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Plaque at the Humboldt University of Berlin: "Max Planck, discoverer of the elementary quantum of action h, taught in this building from 1889 to 1928."
92.
Tonne
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The SI symbol for the tonne is "t", adopted at the same time as the unit itself in 1879. Its use is also official, within the United States, having been adopted by the US National Institute of Standards and Technology. It should not be followed by a period. Abbreviations include "T", "mT", "MT", "mt". In all English-speaking countries that are predominantly metric, tonne is the correct spelling. A full tun, standing about a metre high, could easily weigh a tonne. An English tun of wine weighs 954 kg if full of water, a little less for wine. These terms are now obsolete. The Imperial and US customary units comparable to the tonne are both spelled ton in English, though they differ in mass. One tonne is equivalent to: Metric/SI: 1 megagram. Equal to 7006100000000000000 ♠ 7003100000000000000 ♠ 1000 kilograms. Mg, is the official SI unit. Mg is distinct from milligram. Pounds: Exactly 1000/0.453 592 37 lb, or approximately 7003100000000006859♠2204.622622 lb. US/Short tons: Exactly 1/0.907 184 74 short tons, or approximately 7000110231131100000♠1.102311311 ST.
Tonne
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Base units
93.
Electronvolt
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In physics, the electronvolt is a unit of energy equal to approximately 160 zeptojoules or 1.6×10−19 joules. By definition, it is the amount of energy gained by the charge of a single electron moving across an potential difference of one volt. Thus it is 1 volt multiplied by the elementary charge. Its definition is empirical, thus its value in SI units must be obtained experimentally. Like the elementary charge on which it is based, it is equal to 1 J/C √ 2hα / μ0c0. It is a common unit within physics widely used in solid state, atomic, nuclear, particle physics. It is commonly used with the metric prefixes milli -, kilo -, tera -, peta - or exa -. Thus meV stands for milli-electronvolt. In some older documents, in the Bevatron, the symbol BeV is used, which stands for billion electronvolts; it is equivalent to the GeV. By mass–energy equivalence, the electronvolt is also a unit of mass. The mass equivalent of 1 eV/c2 is 1 eV / c 2 = ⋅ 1 V 2 = 1.783 × 10 − 36 kg. For example, each with a mass of 0.511 MeV/c2, can annihilate to yield 1.022 MeV of energy. The proton has a mass of 0.938 GeV/c2. To convert to megaelectronvolts, use the formula: 1 u = 931.4941 MeV/c2 = 0.9314941 GeV/c2. In high-energy physics, the electronvolt is often used as a unit of momentum.
Electronvolt
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γ: Gamma rays
94.
Particle physics
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Particle physics is the branch of physics that studies the nature of the particles that constitute matter and radiation. By our current understanding, these elementary particles are excitations of the quantum fields that also govern their interactions. The currently dominant theory explaining these fundamental particles and fields, along with their dynamics, is called the Standard Model. In more technical terms, they are described in a Hilbert space, also treated in theory. Their interactions observed to date can be described entirely by a quantum theory called the Standard Model. The Standard Model, as currently formulated, has 61 elementary particles. Those elementary particles can combine to form composite particles, accounting for the hundreds of other species of particles that have been discovered since the 1960s. The Standard Model has been found to agree with almost all the experimental tests conducted to date. However, most particle physicists believe that it is an incomplete description of nature and that a more fundamental theory awaits discovery. In recent years, measurements of neutrino mass have provided the first experimental deviations from the Standard Model. The idea that all matter is composed of elementary particles dates from at least the 6th century BC. In the 19th century, John Dalton, through his work on stoichiometry, concluded that each element of nature was composed of a single, unique type of particle. Throughout the 1950s and 1960s, a bewildering variety of particles were found in scattering experiments. It was referred to informally as the "particle zoo". The current state of the classification of all elementary particles is explained by the Standard Model.
Particle physics
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Large Hadron Collider tunnel at CERN
95.
Atomic mass unit
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The unified atomic mass unit or dalton is the standard unit, used for indicating mass on an atomic or molecular scale. One unified atomic unit is approximately the mass of one nucleon and is numerically equivalent to 1 g/mol. The CIPM has categorised it whose value in SI units must be obtained experimentally. The amu without the "unified" prefix is technically an obsolete unit based on oxygen, replaced in 1961. However, many sources still use the term "amu" but now define it in the same way as u. In this sense, most uses of the terms "mass units" and "amu" today actually refer to unified atomic mass unit. This is also why the mass of a neutron by itself is more than 1 u. The atomic unit is not the unit of mass in the atomic units system, rather the electron rest mass. This evaluation was made prior to the discovery of the existence of elemental isotopes, which occurred in 1912. The divergence of these values was unwieldy. The amu, based on the relative atomic mass of natural oxygen, was about 7000100028199999999 ♠ 1.000282 as massive as the physics amu, based on pure isotopic 16O. For these and other reasons, the standard for both physics and chemistry was changed to carbon-12 in 1961. The choice of carbon-12 was made to minimise further divergence with prior literature. The Dalton is another name for the atomic mass unit. Therefore, in general, "amu" likely does not refer to the old oxygen unit, unless the source material originates from the 1960s or before.
Atomic mass unit
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Base units
96.
Imperial units
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The Imperial Units replaced the Winchester Standards, which were in effect from 1588 to 1825. The system came into official use across the British Empire. The imperial system developed from what were first known as English units, as did the related system of United States customary units. The Weights and Measures Act of 1824 was initially scheduled to go into effect on 1 May 1825. However, the Weights and Measures Act of 1825 pushed back the date to 1 January 1826. The 1824 Act allowed the continued use of pre-imperial units provided that they were customary, widely known, clearly marked with imperial equivalents. Apothecaries' units are mentioned neither in the act of 1824 nor 1825. In Scotland, apothecaries' units were unofficially regulated by the Edinburgh College of Physicians. The three colleges published, at infrequent intervals, Dublin editions having the force of law. The Medical Act of 1858 transferred to The Crown the right to regulate measures. Metric equivalents in this article usually assume the latest official definition. Before this date, the most precise measurement of the imperial Standard Yard was 6999914398416000000♠0.914398416 metres. The Weights and Measures Act of 1985 switched to a gallon of exactly 6997454609000000000♠4.54609 l. These measurements were from 1826 when the imperial gallon was defined, but were officially abolished in the United Kingdom on 1 January 1971. In the USA, though no longer recommended, the apothecaries' system is still used occasionally in medicine, especially in prescriptions for older medications.
Imperial units
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The former Weights and Measures office in Seven Sisters, London.
Imperial units
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Imperial standards of length 1876 in Trafalgar Square, London.
Imperial units
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A baby bottle that measures in three measurement systems—metric, imperial (UK), and US customary.
Imperial units
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A one US gallon gas can purchased near the US-Canada border. It shows equivalences in imperial gallons and litres.
97.
Pound (mass)
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The pound or pound-mass is a unit of mass used in the imperial, United States customary and other systems of measurement. The international standard symbol for the avoirdupois pound is lb. The unit is descended from the Roman libra. The English pound is cognate with, among others, Swedish pund. Usage of the unqualified pound reflects the historical conflation of weight. This accounts for the distinguishing terms pound-force. Countries of the Commonwealth of Nations agreed for the pound and the yard. Since 1 July 1959, the international avoirdupois pound has been defined as exactly 6999453592370000000♠0.45359237 kg. In the United Kingdom, the use of the international pound was implemented in the Weights and Measures Act 1963. An avoirdupois pound is equal to 16 avoirdupois ounces and to exactly 7,000 grains. The libra is an ancient Roman unit of mass, equivalent to approximately 328.9 grams. It was divided into 12 unciae, or ounces. The libra is the origin of the abbreviation for pound, "lb". A number of different definitions of the pound have historically been used in Britain. Amongst these were the obsolete tower, London pounds.
Pound (mass)
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Various historic pounds from a German textbook dated 1848
Pound (mass)
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The Tower Pound
98.
Solar mass
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The solar mass is a standard unit of mass in astronomy, equal to approximately 1.99 × 1030 kilograms. It is used to indicate the masses of other stars, well as clusters, nebulae and galaxies. The value he obtained differs by only 1% from the modern value. The diurnal parallax of the Sun was accurately measured in 1761 and 1769 yielding a value of 6995436332312998583 ♠ 9 ″. From the value of the diurnal parallax, one can determine the distance from the geometry of Earth. The first person to estimate the mass of the Sun was Isaac Newton. In his Principia, he estimated that the ratio of the mass of Earth to the Sun was about 1/28 700. He corrected his estimated ratio in the third edition of the Principia. The current value for the solar parallax is smaller still, yielding an estimated ratio of 1/332 946. As a unit of measurement, the solar mass came into use before the gravitational constant were precisely measured. The mass of the Sun has decreased since the time it formed. This has occurred through two processes in nearly equal amounts. Most of this energy eventually radiates away from the Sun. Second, high-energy electrons in the atmosphere of the Sun are ejected directly into outer space as a solar wind. The original mass of the Sun at the time it reached the main sequence remains uncertain.
Solar mass
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Internal structure
Solar mass
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Size and mass of very large stars: Most massive example, the blue Pistol Star (150 M ☉). Others are Rho Cassiopeiae (40 M ☉), Betelgeuse (20 M ☉), and VY Canis Majoris (17 M ☉). The Sun (1 M ☉) which is not visible in this thumbnail is included to illustrate the scale of example stars. Earth's orbit (grey), Jupiter's orbit (red), and Neptune's orbit (blue) are also given.
99.
Sun
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The Sun is the star at the center of the Solar System. It is a nearly perfect sphere of hot plasma, with internal motion that generates a magnetic field via a dynamo process. It is by far the most important source of energy for life on Earth. The Sun is informally referred to as a yellow dwarf. It formed approximately 4.6 billion years ago within a region of a large molecular cloud. Most of this matter gathered in the center, whereas the rest flattened into an orbiting disk that became the Solar System. The central mass became so dense that it eventually initiated nuclear fusion in its core. It is thought that almost all stars form by this process. After fusion in its core has stopped, the Sun will undergo severe changes and become a red giant. It is calculated that the Sun will become sufficiently large to engulf the current orbits of Mercury, possibly Earth. The Sun has been regarded by some cultures as a deity. Its orbit around the Sun are the basis of the solar calendar, the predominant calendar in use today. The English proper name Sun may be related to south. All Germanic terms for the Sun stem from Proto-Germanic *sunnōn. The Latin name for Sol, is not common in general English language use; the adjectival form is the related word solar.
Sun
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The Sun in visible wavelength with filtered white light on 8 July 2014. Characteristic limb darkening and numerous sunspots are visible.
Sun
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During a total solar eclipse, the solar corona can be seen with the naked eye, during the brief period of totality.
Sun
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Taken by Hinode 's Solar Optical Telescope on 12 January 2007, this image of the Sun reveals the filamentary nature of the plasma connecting regions of different magnetic polarity.
Sun
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Visible light photograph of sunspot, 13 December 2006
100.
Compton wavelength
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The Compton wavelength is a quantum mechanical property of a particle. It was introduced by electrons. The Compton wavelength of a particle is equivalent to the wavelength of a photon whose energy is the same as the mass of the particle. The significance of this formula is shown in the derivation of the Compton formula. The CODATA 2014 value for the Compton wavelength of the electron is 6988242631023670000 2.4263102367 × 10 − 12 m. Other particles have different Compton wavelengths. It appears in the Dirac equation: − i γ μ ∂ ψ + ψ = 0. The reduced Compton wavelength also appears in Schrödinger's equation, although its presence is obscured in traditional representations of the equation. The reduced Compton wavelength is a natural representation for mass on the scale. Equations that pertain to inertial mass like Klein-Gordon and Schrödinger's, use the reduced Compton wavelength. The non-reduced Compton wavelength is a natural representation for mass, converted into energy. Equations that pertain into energy, or to the wavelengths of photons interacting with mass, use the non-reduced Compton wavelength. A particle of mass m has a energy of E = mc2. The non-reduced Compton wavelength for this particle is the wavelength of a photon of the same energy. The Compton wavelength expresses a fundamental limitation on taking into account quantum mechanics and special relativity.
Compton wavelength
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The Schwarzschild radius (r s) represents the ability of mass to cause curvature in space and time.
101.
Black hole
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The theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of the region from which no escape is possible is called the event horizon. Although the event horizon has an enormous effect on the fate and circumstances of an object crossing it, no locally detectable features appear to be observed. In many ways a black hole acts like an ideal black body, as it reflects no light. This temperature is on the order of billionths of a kelvin for black holes of stellar mass, making it essentially impossible to observe. Objects whose gravitational fields are too strong for light to escape were first considered by Pierre-Simon Laplace. Black holes were long considered a mathematical curiosity; it was during the 1960s that theoretical work showed they were a generic prediction of general relativity. The discovery of neutron stars sparked interest as a astrophysical reality. Black holes of stellar mass are expected to form when very massive stars collapse at the end of their life cycle. After a black hole has formed, it can continue to grow by absorbing mass from its surroundings. By merging with black holes, supermassive black holes of millions of solar masses may form. There is general consensus that supermassive black holes exist in the centers of most galaxies. Matter that falls onto a black hole can form an external accretion disk heated by friction, forming some of the brightest objects in the universe. If there are other stars orbiting a black hole, their orbits can be used to determine the black hole's mass and location. Such observations can be used to exclude possible alternatives such as neutron stars.
Black hole
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Predicted appearance of non-rotating black hole with toroidal ring of ionised matter, such as has been proposed as a model for Sagittarius A*. The asymmetry is due to the Doppler effect resulting from the enormous orbital speed needed for centrifugal balance of the very strong gravitational attraction of the hole.
Black hole
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Simulation of gravitational lensing by a black hole, which distorts the image of a galaxy in the background
Black hole
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A simple illustration of a non-spinning black hole
Black hole
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A simulated event in the CMS detector, a collision in which a micro black hole may be created.
102.
Schwarzschild radius
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An example of an object where the mass is within its Schwarzschild radius is a black hole. Once a stellar remnant collapses to or below this radius, light cannot escape and the object is no longer directly visible, thereby forming a black hole. It is a characteristic radius associated with every quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916. In 1916, Karl Schwarzschild obtained the exact solution for the gravitational field outside a non-rotating, symmetric body. The Schwarzschild radius of an object is proportional to the mass. Accordingly, the Sun has a Schwarzschild radius of approximately 3.0 km, whereas Earth's is only about 9.0 mm. The universe's mass has a Schwarzschild radius of approximately billion light years. See Deriving the Schwarzschild solution. Any object whose radius is smaller than its Schwarzschild radius is called a black hole. The surface at the Schwarzschild radius acts as an event horizon in a non-rotating body. Neither particles can escape through this surface from the inside, hence the name "black hole". Black holes can be classified based on their Schwarzschild radius, or equivalently, by their density. The volume enclosed in the event horizon of the most massive black holes has a density lower than main sequence stars. Unlike black holes, supermassive black holes have comparatively low densities.
Schwarzschild radius
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The Schwarzschild radius (r s) represents the ability of mass to cause curvature in space and time.
103.
Standard gravitational parameter
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μ = G M For several objects in the Solar System, the value of μ is known to greater accuracy than either G or M. The SI units of the gravitational parameter are m3 s − 2. This approximation is standard for planets orbiting most moons and greatly simplifies equations. Conversely, measurements of the smaller body's orbit only provide information on the product, μ, M separately. For parabolic trajectories rv2 is equal to 2μ. For hyperbolic orbits μ = 2a | ε |, where ε is the specific orbital energy. The value for the Earth equals 7005398600441800000 ♠ 398600.4418 ± 0.0008 km3 s − 2. The uncertainty of those measures is 1 to 7003700000000000000♠7000, so M will have the same uncertainty. The value for the Sun equals 7020132712440018000 ♠ 1.32712440018 × 1020 m3 s − 2. Note that the reduced mass is also denoted by μ. Astronomical system of units Planetary mass
Standard gravitational parameter
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The Schwarzschild radius (r s) represents the ability of mass to cause curvature in space and time.
104.
Physical science
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Physical science is a branch of natural science that studies non-living systems, in contrast to life science. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". In natural science, hypotheses must be verified scientifically to be regarded as scientific theory. Validity, social mechanisms ensuring quality control, such as peer review and repeatability of findings, are amongst the criteria and methods used for this purpose. Natural science can be broken for example biology and physical science. All of their sub-branches, are referred to as natural sciences. Branches of astronomy Chemistry – studies the composition, structure, properties and change of matter. Branches of chemistry Earth science – all-embracing term referring to the fields of science dealing with planet Earth. Earth science is the study of how it evolved to its current state. It includes the study of hydrosphere, lithosphere, biosphere. Branches of Earth science History of physical science – history of the branch of natural science that studies non-living systems, in contrast to the biological sciences. It in turn has many branches, each referred to as a "physical science", together called the "physical sciences". However, the term "physical" creates an unintended, somewhat arbitrary distinction, since many branches of physical science also study biological phenomena. History of astrodynamics – history of the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. History of astrometry – history of the branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies.
Physical science
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Chemistry, the central science, partial ordering of the sciences proposed by Balaban and Klein.
105.
Proportionality (mathematics)
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The constant is called the coefficient of proportionality or proportionality constant. If one variable is always the product of a constant, the two are said to be directly proportional. X and y are directly proportional if the y/x is constant. If the product of the two variables is always a constant, the two are said to be inversely proportional. X and y are inversely proportional if the xy is constant. To express the statement "y is directly proportional to x" where c is the proportionality constant. Symbolically, this is written as y ∝ x. To express the statement "y is inversely proportional to x" mathematically, we write an equation y = c/x. We can equivalently write "y is directly proportional to 1/x". An equality of two ratios is called a proportion. For example, a/c = b/d, where no term is zero. Given two variables x and y, y is directly proportional to x if there is a constant k such that y = k x. The circumference of a circle is directly proportional to its diameter, with the constant of proportionality equal to π. The concept of inverse proportionality can be contrasted against direct proportionality. Consider two variables said to be "inversely proportional" to each other.
Proportionality (mathematics)
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Variable y is directly proportional to the variable x.
106.
Electrophoretic deposition
–
All colloidal particles that can be used to form stable suspensions and that can carry a charge can be used in electrophoretic deposition. This includes materials such as polymers, pigments, dyes, ceramics and metals. The process is useful for applying materials to any electrically conductive surface. The materials which are being deposited are the major determining factor in the actual processing conditions and equipment which may be used. Due to the wide utilization of electrophoretic painting processes in many industries, aqueous EPD is the most common commercially used EPD process. However, non-aqueous electrophoretic deposition applications are known. Applications of non-aqueous EPD are currently being explored for use in the fabrication of electronic components and the production of ceramic coatings. Non-aqueous processes have the advantage of avoiding the electrolysis of water and the oxygen evolution which accompanies electrolysis. This process is industrially used for applying coatings to metal fabricated products. Thick films produced this way allow cheaper and more rapid synthesis relative to sol-gel thin-films, along with higher levels of photocatalyst surface area. In the fabrication of solid oxide fuel cells EPD techniques are widely employed for the fabrication of porous ZrO2 anodes from powder precursors onto conductive substrates. Complex fabricated objects can easily be coated, both inside cavities as well as on the outside surfaces. Relatively high speed of coating. Relatively high purity. Applicability to wide range of materials Easy control of the coating composition.
Electrophoretic deposition
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Electrophoretic Deposition Process
107.
Free-fall
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In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. The present article only concerns itself with free fall in the Newtonian domain. An object in the technical sense of free fall may not necessarily be falling down in the usual sense of the term. The moon is thus in free fall. A body in free fall experiences "0 g". The term "free fall" is often used more loosely in the strict sense defined above. Thus, lifting device, is also often referred to as free fall. The Greek philosopher Aristotle discussed falling objects in what was perhaps the first book on mechanics. The Italian scientist Galileo Galilei subjected the Aristotelian theories to experimentation and careful observation. He then combined the results of these experiments with mathematical analysis in an unprecedented way. In a tale that may be apocryphal, Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things enough to the point where he was able to measure the time intervals with water clocks and his own pulse. Examples of objects in free fall include: A spacecraft with propulsion off.
Free-fall
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Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of, where h is the height and g is the free-fall acceleration due to gravity.
Free-fall
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Acceleration of a small meteoroid when entering the Earth's atmosphere at different initial velocities.
Free-fall
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Joseph Kittinger starting his record-breaking skydive in 1960. His record was broken only in 2012.
108.
Moon
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The Moon is Earth's only permanent natural satellite. It is the largest among planetary satellites relative to the size of the planet that it orbits. It is the second-densest satellite among those whose densities are known. The average distance of the Moon from the Earth is 1.28 light-seconds. The Moon is thought to have formed not long after Earth. It is the second-brightest regularly visible celestial object in Earth's sky, as measured by illuminance on Earth's surface. Its surface is actually dark, although compared to the sky it appears very bright, with a reflectance just slightly higher than that of worn asphalt. The Moon's gravitational influence produces the ocean tides, the slight lengthening of the day. This matching of visual size will not continue in the far future. This rate is not constant. Since the Apollo 17 mission in 1972, the Moon has been visited only by uncrewed spacecraft. The usual proper name for Earth's natural satellite is "the Moon". Occasionally, the name "Luna" is used. The principal English adjective pertaining to the Moon is lunar, derived from the Latin Luna. A less common adjective is selenic, derived from, derived the prefix "seleno -".
Moon
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Full moon as seen from Earth's northern hemisphere
Moon
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The Moon, tinted reddish, during a lunar eclipse
Moon
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Near side of the Moon
Moon
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Far side of the Moon
109.
Pair production
–
However, all other conserved quantum numbers of the produced particles must sum to zero – thus the created particles shall have opposite values of each other. The probability of production in photon-matter interactions also increases approximately as the square of atomic number of the nearby atom. For photons with high energy, production is the dominant mode of photon interaction with matter. These interactions were first observed in Patrick Blackett's counter-controlled cloud chamber, leading to the 1948 Nobel Prize in Physics. The photon must have higher energy than the sum of the mass energies of an positron for the production to occur. Because of this, when pair production occurs, the atomic nucleus receives some recoil. The reverse of this process is electron positron annihilation. These properties can be derived through the kinematics of the interaction. This derivation is a semi-classical approximation. An exact derivation of the kinematics can be done taking into account the mechanical scattering of photon and nucleus. Cross sections are tabulated for different materials and energies. In 2008 the Titan laser aimed at a 1-millimeter-thick gold target was used to generate positron–electron pairs in large numbers. Pair production is invoked to predict the existence of hypothetical Hawking radiation. According to quantum mechanics, particle pairs are constantly disappearing as a foam. When this happens in the region around a black hole, one particle may escape while its antiparticle partner is captured by the black hole.
Pair production
–
Light–matter interaction
110.
Nuclear fusion
–
The difference in mass between the reactants is manifested as the release of large amounts of energy. This difference in mass arises due to the difference in atomic "binding energy" between the atomic nuclei after the reaction. Fusion is other high magnitude stars. The process that produces a nucleus lighter than iron-56 or nickel-62 will generally yield a net energy release. These elements have the largest binding energy per nucleon, respectively. The opposite is true for nuclear fission. The astrophysical event of a supernova can produce enough energy to fuse nuclei into elements heavier than iron. During the remainder of that decade the steps of the main cycle of nuclear fusion in stars were worked out by Hans Bethe. Research into fusion for military purposes began as part of the Manhattan Project. Fusion was accomplished with the Greenhouse Item nuclear test. Nuclear fusion on a large scale in an explosion was first carried out in the Ivy Mike hydrogen bomb test. It continues to this day. They nonetheless stick together, demonstrating the existence of another force referred to as nuclear attraction. This force, called the nuclear force, overcomes electric repulsion at very close range. The effect of this force is not observed outside the nucleus, hence the force is called a short-range force.
Nuclear fusion
–
The Sun is a main-sequence star, and thus generates its energy by nuclear fusion of hydrogen nuclei into helium. In its core, the Sun fuses 620 million metric tons of hydrogen each second.
Nuclear fusion
–
The Tokamak à configuration variable, research fusion reactor, at the École Polytechnique Fédérale de Lausanne (Switzerland).
Nuclear fusion
–
The only man-made fusion device to achieve ignition to date is the hydrogen bomb. [citation needed] The detonation of the first device, codenamed Ivy Mike, occurred in 1952 and is shown here.
111.
Gravitational lens
–
The amount of bending is one of the predictions of Albert Einstein's general theory of relativity. Fritz Zwicky posited in 1937 that the effect could allow galaxy clusters to act as gravitational lenses. It was not until 1979 that this effect was confirmed by observation of the so-called "Twin QSO" SBS +561. Consequently, a gravitational lens has a focal line. The term "lens" in the context of gravitational light deflection was first used by O.J. Lodge, who remarked that it is "not permissible to say that the solar gravitational field acts like a lens, for it has no focal length". If there is any misalignment, the observer will see an segment instead. This phenomenon was first quantified by Albert Einstein in 1936. There are three classes of gravitational lensing: 1. Strong lensing: where there are easily visible distortions such as the formation of Einstein rings, arcs, multiple images. 2. The lensing shows up statistically as a preferred stretching of the background objects perpendicular to the direction to the center of the lens. This, in turn, can be used to reconstruct the mass distribution in the area: in particular, the distribution of dark matter can be reconstructed. Since the weak gravitational lensing signal is small, a very large number of galaxies must be used in these surveys. They may also provide an future constraint on dark energy.
Gravitational lens
–
Gravitational lensing
Gravitational lens
–
One of Eddington 's photographs of the 1919 solar eclipse experiment, presented in his 1920 paper announcing its success
Gravitational lens
–
Bending light around a massive object from a distant source. The orange arrows show the apparent position of the background source. The white arrows show the path of the light from the true position of the source.
Gravitational lens
–
In the formation known as Einstein's Cross, four images of the same distant quasar appear around a foreground galaxy due to strong gravitational lensing.
112.
Spacetime
–
In physics, spacetime is any mathematical model that combines space and time into a single interwoven continuum. In cosmology, the concept of spacetime combines time to a single abstract universe. Mathematically it is a manifold whose points correspond to physical events. In a coordinate system whose domain is an open set of the spacetime manifold, three spacelike coordinates and one timelike coordinate typically emerge. Dimensions are independent components of a coordinate grid needed to locate a point in a certain defined "space". On the globe the latitude and longitude are two independent coordinates which together uniquely determine a location. In spacetime, a coordinate grid that spans the +1 dimensions locates events, i.e. time is added as another dimension to the coordinate grid. This the coordinates specify where and when events occur. Unlike in spatial coordinates, there are still restrictions for how measurements can be made spatially and temporally. These restrictions correspond roughly to a mathematical model which differs from Euclidean space in its manifest symmetry. Such slowing, called dilation, is explained in special relativity theory. The duration of time can therefore vary according to events and reference frames. The spacetime has taken on a generalized meaning beyond treating spacetime events with the normal 3 +1 dimensions. It is really the combination of time. How many dimensions are needed to describe the universe is still an open question.
Spacetime
–
Key concepts
113.
Curvature
–
In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry. This article deals primarily with extrinsic curvature. Its canonical example is that of a circle, which has a curvature equal to the reciprocal of its radius everywhere. Smaller circles bend more sharply, hence have higher curvature. The curvature of a smooth curve is defined as the curvature of its osculating circle at each point. The curvature of more complex objects is described from linear algebra, such as the general Riemann curvature tensor. This article sketches the mathematical framework which describes the curvature of a curve embedded in the curvature of a surface in Euclidean space. Let C be a curve. The curvature of C at a point is a measure of how sensitive its line is to moving the point to other nearby points. There are a number of equivalent ways that this idea can be made precise. One way is geometrical. It is natural to define the curvature of a straight line to be constantly zero. The curvature of a circle of radius R should be large if R is small if R is large. Thus the curvature of a circle is defined to be the reciprocal of the radius: κ = 1 R. The curvature of C at P is then defined to be the curvature of that line.
Curvature
114.
Atomic clocks
–
Early atomic clocks were based on masers at room temperature. An example of this is frequency standards of the United States. The accuracy of an atomic clock depends on two factors. The first factor is temperature of the sample atoms—colder atoms move much more slowly, allowing longer probe times. The second factor is the frequency and intrinsic width of the electronic transition. Higher frequencies and narrow lines increase the precision. National agencies in many countries maintain a network of atomic clocks which are kept synchronized to an accuracy of 10 − 9 seconds per day. These clocks collectively define a continuous and stable time scale, International Atomic Time. For civil time, another time scale is disseminated, Coordinated Universal Time. The idea of using atomic transitions to measure time was suggested by Lord Kelvin in 1879. Magnetic resonance, developed in the 1930s by Isidor Rabi, became the practical method for doing this. In 1945, Rabi first publicly suggested that magnetic resonance might be used as the basis of a clock. The atomic clock was an ammonia device built in 1949 at the U.S. National Bureau of Standards. It was less accurate than existing quartz clocks, but served to demonstrate the concept. Calibration of the atomic clock was carried out by the use of the astronomical time scale ephemeris time.
Atomic clocks
–
FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.
Atomic clocks
–
The master atomic clock ensemble at the U.S. Naval Observatory in Washington, D.C., which provides the time standard for the U.S. Department of Defense. The rack mounted units in the background are Symmetricom (formerly HP) 5071A caesium beam clocks. The black units in the foreground are Symmetricom (formerly Sigma-Tau) MHM-2010 hydrogen maser standards.
Atomic clocks
–
Louis Essen (right) and Jack Parry (left) standing next to the world's first caesium-133 atomic clock.
Atomic clocks
–
Chip-scale atomic clocks, such as this one unveiled in 2004, are expected to greatly improve GPS location.
115.
Gravitational time dilation
–
The weaker the gravitational potential, the faster time passes. It has since been confirmed by tests of general relativity. This has been demonstrated by noting that atomic clocks at differing altitudes will eventually show different times. The effects detected in Earth-bound experiments are extremely small, with differences being measured in nanoseconds. Demonstrating larger effects would require greater distances from a larger gravitational source. Gravitational dilation was first described by Albert Einstein in 1907 as a consequence of special relativity in accelerated frames of reference. The existence of gravitational dilation was first confirmed directly by the Pound -- Rebka experiment in 1959. Clocks that are far from massive bodies run clocks close to massive bodies run more slowly. Let us consider a family of observers along a straight "vertical" line, each of whom experiences a constant g-force along this line. Let g be the dependence of g-force on a coordinate along the aforementioned line. See Ehrenfest paradox for application of the same formula to a rotating frame in flat space-time. In comparison, a clock on the surface of the sun will accumulate around 66.4 fewer seconds in one year. In the Schwarzschild metric, free-falling objects can be in circular orbits if the orbital radius is larger than 2 r s. The formula for a clock at rest is given above; for a clock in a circular orbit, the formula is instead. T 0 = t f 1 − 2 ⋅ r s r.
Gravitational time dilation
–
Key concepts
Gravitational time dilation
–
Satellite clocks are slowed by their orbital speed but sped up by their distance out of the Earth's gravitational well.
116.
Gravity Probe B
–
Gravity Probe B was a satellite-based mission which launched on 20 April 2004 on a Delta II rocket. The phase lasted until 2005; its aim was to measure spacetime curvature near Earth, thereby the stress -- tensor in and near Earth. This provided a test of general relativity, gravitomagnetism and related models. The principal investigator was Francis Everitt. Initial results confirmed the expected geodetic effect to an accuracy of about 1%. The expected frame-dragging effect was similar in magnitude to the current noise level. Work continued to model and account for these sources of error, thus permitting extraction of the frame-dragging signal. On 19 November 2015, the Institute of Physics Classical and Quantum Gravity Journal published a special focus issue devoted exclusively to Gravity Probe B. Gravity Probe B was a relativity gyroscope experiment funded by NASA. Efforts were led by Stanford University physics department with Lockheed Martin as the primary subcontractor. Mission scientists viewed it as the second gravity experiment in space, following the successful launch of Gravity Probe A in 1976. The mission plans were to test two unverified predictions of general relativity: the geodetic effect and frame-dragging. The gyroscopes were intended to be so free from disturbance that they would provide a space-time system. The geodetic effect is an effect caused by space-time being "curved" by the mass of the Earth. A gyroscope's axis when parallel transported around the Earth in one complete revolution does not end up pointing in exactly the same direction as before.
Gravity Probe B
–
Gravity Probe B
Gravity Probe B
–
Gravity Probe B with solar panels folded.
Gravity Probe B
–
At the time, the fused quartz gyroscopes created for Gravity Probe B were the most nearly perfect spheres ever created by humans. The gyroscopes differ from a perfect sphere by no more than 40 atoms of thickness, refracting the image of Einstein in background.
Gravity Probe B
117.
Frequency
–
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency, which emphasizes the contrast to spatial frequency. The period is the duration of time of one cycle in a repeating event, so the period is the reciprocal of the frequency. For example, if a newborn baby's heart beats at a frequency of a minute, its period -- the interval between beats -- is half a second. For cyclical processes, such as waves, frequency is defined as a number of cycles per unit time. Period X Ordinary frequency = 1 cycle. Therefore, the period, usually denoted by T, is the reciprocal of the frequency f: f = 1 T. The SI unit of frequency is the hertz, named after the German physicist Heinrich Hertz; one hertz means that an event repeats once per second. A previous name for this unit was cycles per second. The SI unit for period is the second. A traditional unit of measure used with rotating mechanical devices is revolutions per abbreviated rpm. 60 rpm equals one hertz. As a matter of convenience, slower waves, such as surface waves, tend to be described by wave period rather than frequency. Fast waves, like radio, are usually described by their frequency instead of period. Spatial frequency is analogous to temporal frequency, but the time axis is replaced by one or more spatial displacement axes.
Frequency
–
A resonant-reed frequency meter, an obsolete device used from about 1900 to the 1940s for measuring the frequency of alternating current. It consists of a strip of metal with reeds of graduated lengths, vibrated by an electromagnet. When the unknown frequency is applied to the electromagnet, the reed which is resonant at that frequency will vibrate with large amplitude, visible next to the scale.
Frequency
–
As time elapses – represented here as a movement from left to right, i.e. horizontally – the five sinusoidal waves shown vary regularly (i.e. cycle), but at different rates. The red wave (top) has the lowest frequency (i.e. varies at the slowest rate) while the purple wave (bottom) has the highest frequency (varies at the fastest rate).
Frequency
Frequency
–
Modern frequency counter
118.
Spectroscopy
–
Spectroscopy /spɛkˈtrɒskəpi/ is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency. Spectroscopic data is often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency. Spectral measurement devices are referred to as spectrometers, spectrophotometers, spectrographs or spectral analyzers. Daily observations of color can be related to spectroscopy. Neon lighting is a direct application of atomic spectroscopy. Neon and other noble gases have characteristic emission frequencies. Neon lamps use collision of electrons with the gas to excite these emissions. Paints include chemical compounds selected for their spectral characteristics in order to generate specific hues. A commonly encountered molecular spectrum is that of nitrogen dioxide. This gives a reddish-brown color. Rayleigh scattering is a spectroscopic scattering phenomenon that accounts for the color of the sky. Spectroscopy is used in physical and analytical chemistry because atoms and molecules have unique spectra. As a result, these spectra can be used to quantify information about the molecules.
Spectroscopy
–
Analysis of white light by dispersing it with a prism is an example of spectroscopy.
Spectroscopy
–
A huge diffraction grating at the heart of the ultra-precise ESPRESSO spectrograph.
Spectroscopy
–
UVES is a high-resolution spectrograph on the Very Large Telescope.
119.
Watt balance
–
The weight of the kilogram is then used to compute the mass of the kilogram by accurately determining the gravitational acceleration. This will define the mass of a kilogram in terms of a voltage, as described below. The main weakness of the ampere method is that the result depends on the accuracy with which the dimensions of the coils are measured. This extra step involves moving the coil through a known magnetic flux at a known speed. This step was done in 1990. In 2014, NRC researchers published the most accurate measurement of the Planck constant with a relative uncertainty of 1.8 × 10 − 8. In the balance, the current is varied so that this force exactly counteracts the weight w of a standard mass m. This is also the principle behind the ampere balance. W is given by the mass m multiplied by the local gravitational acceleration g. Thus w = m g = B L I. Kibble's watt balance avoids the problems of measuring B and L with a second calibration step. Thus V = B L v. The unknown product BL can be eliminated from the equations to give V I = m g v. With V, I, g, v accurately measured, this gives an accurate value for m. Both sides of the equation have the dimensions of power, measured in watts in the International System of Units; hence the name "watt balance".
Watt balance
–
The NIST watt balance; the vacuum chamber dome, which lowers over the entire apparatus, is visible at top
Watt balance
–
Precision Ampere balance at the US National Bureau of Standards (now NIST) in 1927. The current coils are visible under the balance, attached to the right balance arm. The Watt balance is a development of the Ampere balance.
120.
Mass versus weight
–
In common usage, the mass of an object is often referred to as its weight, though these are in fact different concepts and quantities. In scientific contexts, mass refers loosely to the amount of "matter" in an object, whereas weight refers to the force exerted by gravity. In other words, an object with a mass of 1.0 kilogram will weigh approximately 9.81 newtons on the surface of the Earth. Objects on the surface of the Earth have weight, although sometimes this weight is difficult to measure. Thus, the "weightless object" floating in water actually transfers its weight to the bottom of the container. Similarly, a balloon may appear to have no weight or even negative weight, due to buoyancy in air. The weight of a flying airplane does not disappear. Such a force constitutes weight. This force can be added to by any other kind of force. In the photograph, the girl's weight, subtracted from the tension in the chain, yields the necessary force to keep her swinging in an arc. Accordingly, for an astronaut on a spacewalk in orbit, no effort is required to hold a communications satellite in front of him; it is "weightless". On Earth, a seat can demonstrate this relationship between force, mass, acceleration. Applying the same impetus to a small child would produce a much greater speed. Mass is an inertial property;, the tendency of an object to remain at constant velocity unless acted upon by an outside force. Inertia is seen when a ball is pushed horizontally on a level, smooth surface, continues in horizontal motion.
Mass versus weight
–
If one were to stand behind this girl at the bottom of the arc and try to stop her, one would be acting against her inertia, which arises from mass, not weight.
Mass versus weight
–
Matter's mass strongly influences many familiar kinetic properties.
Mass versus weight
–
A hot air balloon when it has neutral buoyancy has no weight for the men to support but still retains its great mass and inertia.
Mass versus weight
–
A balance-type weighing scale: Unaffected by the strength of gravity.
121.
Gravity of Earth
–
In SI units this acceleration is measured in newtons per kilogram. There is the downwards force experienced by objects on Earth, given by the equation F = ma. However, other factors such as the rotation of the Earth also contribute to the net acceleration. The precise strength of Earth's gravity varies depending on location. The nominal "average" value at the Earth's surface, known as standard gravity is, by definition, 9.80665 m/s2. This quantity is denoted variously as gn, ge, g0, simply g. The Earth is slightly flatter at the poles while bulging at the Equator: an oblate spheroid. There are consequently slight deviations of gravity across its surface. The net force as measured by a scale and bob is called "effective gravity" or "apparent gravity". Effective gravity includes other factors that affect the net force. These factors include things such as centrifugal force at the surface from the Earth's rotation and the gravitational pull of the Moon and Sun. In large cities, it ranges to 9.825 in Oslo and Helsinki. The surface of the Earth is rotating, so it is not an inertial frame of reference. At latitudes nearer the Equator, the centrifugal force produced by Earth's rotation is larger than at polar latitudes. The same two factors influence the direction of the effective gravity.
Gravity of Earth
–
Earth's gravity measured by NASA's GRACE mission, showing deviations from the theoretical gravity of an idealized smooth Earth, the so-called earth ellipsoid. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker. (Animated version.)
Gravity of Earth
–
Earth's radial density distribution according to the Preliminary Reference Earth Model (PREM).
122.
Kilograms
–
The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimeter of water at the melting point of ice. The kilogram is the only SI base unit with an SI prefix as part of its name. Three other base units and 17 derived units in the SI system are defined relative to the kilogram, so its stability is important. Only 8 other units do not require the kilogram in their definition: angle. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting. There are currently several different proposals for the redefinition; these are described in the Proposed Future Definitions section below. The International Prototype Kilogram is rarely used or handled. In the decree of 1795, the term gramme thus replaced gravet, kilogramme replaced grave. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common. UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling. The kilogram is a unit of mass, a property which corresponds to the common perception of how "heavy" an object is. Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor; they are "weightless". The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses. Accordingly, a provisional mass standard was made as a single-piece, metallic artifact one thousand times as massive as the gram—the kilogram.
Kilograms
–
A domestic-quality one-kilogram weight made of cast iron (the credit card is for scale). The shape follows OIML recommendation R52 for cast-iron hexagonal weights
Kilograms
–
Measurement of weight – gravitational attraction of the measurand causes a distortion of the spring
Kilograms
–
Measurement of mass – the gravitational force on the measurand is balanced against the gravitational force on the weights.
Kilograms
–
The Arago kilogram, an exact copy of the "Kilogramme des Archives" commissioned in 1821 by the US under supervision of French physicist François Arago that served as the US's first kilogram standard of mass until 1889, when the US converted to primary metric standards and received its current kilogram prototypes, K4 and K20.
123.
Newtons
–
The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion. See below for the conversion factors and unitizing. In 1948, the 9th CGPM resolution 7 adopted the name "newton" for this force. The MKS system then became the blueprint for today's SI system of units. The newton thus became International System of Units. This SI unit is named after Isaac Newton. As with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2. The newton is therefore: where the following symbols are used for the units: kg for kilogram, m for metre, s for second. In dimensional analysis: F = M L T 2 where F is force, M is mass, L is length and T is time. At average gravity on earth, a mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apple's weight. 441 N = 45 kg × 9.80665 m/s2 It is common to see forces expressed in kilonewtons where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train and the thrust of an F100 fighter jet are both around 130 kN.
Newtons
–
Base units
124.
Free fall
–
In Newtonian physics, free fall is any motion of a body where gravity is the only force acting upon it. The present article only concerns itself with free fall in the Newtonian domain. An object in the technical sense of free fall may not necessarily be falling down in the usual sense of the term. The moon is thus in free fall. A body in free fall experiences "0 g". The term "free fall" is often used more loosely in the strict sense defined above. Thus, lifting device, is also often referred to as free fall. The Greek philosopher Aristotle discussed falling objects in what was perhaps the first book on mechanics. The Italian scientist Galileo Galilei subjected the Aristotelian theories to experimentation and careful observation. He then combined the results of these experiments with mathematical analysis in an unprecedented way. In a tale that may be apocryphal, Galileo dropped two objects of unequal mass from the Leaning Tower of Pisa. Given the speed at which such a fall would occur, it is doubtful that Galileo could have extracted much information from this experiment. Most of his observations of falling bodies were really of bodies rolling down ramps. This slowed things enough to the point where he was able to measure the time intervals with water clocks and his own pulse. Examples of objects in free fall include: A spacecraft with propulsion off.
Free fall
–
Measured fall time of a small steel sphere falling from various heights. The data is in good agreement with the predicted fall time of, where h is the height and g is the free-fall acceleration due to gravity.
Free fall
Free fall
–
Acceleration of a small meteoroid when entering the Earth's atmosphere at different initial velocities.
Free fall
–
Joseph Kittinger starting his record-breaking skydive in 1960. His record was broken only in 2012.
125.
Weightlessness
–
This is also termed "zero-g" where the term is more correctly understood as meaning "zero g-force." In such cases, a sensation of weight, in the sense of a state of stress can occur, even if the gravitational field were zero. In such cases, bodies are not weightless. When the gravitational field is non-uniform, a body in free fall is not stress-free. Near a black hole, tidal effects can be very strong. It prevails in orbiting spacecraft. In October 2015, the NASA Office of Inspector General issued a health hazards report related to human spaceflight, including a human mission to Mars. In Newtonian mechanics the term "weight" is given two distinct interpretations by engineers. Weightlessness in this sense can be achieved by removing the body away from the source of gravity. It can also be attained by placing the body at a neutral point between two gravitating masses. Weight2: Weight can also be interpreted as that quantity, measured when one uses scales. What is being measured there is the force exerted by the body on the scales. By Newton's 3rd law, there is an opposite force exerted by the body on the machine. This force is called weight2. The force is not gravitational.
Weightlessness
–
Astronauts on the International Space Station experience only microgravity and thus display an example of weightlessness. Michael Foale can be seen exercising in the foreground.
Weightlessness
–
Zero gravity flight maneuver
Weightlessness
–
NASA's KC-135A plane ascending for a zero gravity maneuver
Weightlessness
–
Zero-gravity testing at the NASA Zero Gravity Research Facility
126.
Earth
–
According to radiometric dating and other sources of evidence, Earth formed about billion years ago. Earth gravitationally interacts with other objects in space, the Moon. During one orbit around the Sun, Earth rotates about its axis 366.26 times, creating sidereal year. Earth's lithosphere is divided into several tectonic plates that migrate across the surface over periods of many millions of years. 71% of Earth's surface is covered with water. The remaining 29 % is mass -- consisting of continents and islands -- that together has many lakes, rivers, other sources of water that contribute to the hydrosphere. The majority of Earth's polar regions are covered including the Antarctic ice sheet and the sea ice of the Arctic ice pack. Some geological evidence indicates that life may have arisen as much as billion years ago. Since then, the combination of Earth's distance from the Sun, geological history have allowed life to evolve and thrive. In the history of the Earth, biodiversity has gone through long periods of expansion, occasionally punctuated by mass extinction events. Over 99% of all the species of life that ever lived on Earth are extinct. Estimates of the number of species on Earth today vary widely; most species have not been described. Over billion humans live on Earth and depend on its biosphere and minerals for their survival. Humanity has developed diverse cultures; politically, the world is divided into about 200 sovereign states. The English word Earth developed from a wide variety of Middle English forms, which derived from an Old English noun most often spelled eorðe.
Earth
–
" The Blue Marble " photograph of Earth, taken during the Apollo 17 lunar mission in 1972
Earth
–
Artist's impression of the early Solar System's planetary disk
Earth
–
World map color-coded by relative height
Earth
–
The summit of Chimborazo, in Ecuador, is the point on Earth's surface farthest from its center.
127.
Earth's gravity
–
In SI units this acceleration is measured in metres per second squared or equivalently in newtons per kilogram. There is the downwards force experienced given by the equation F = ma. However, other factors such as the rotation of the Earth also contribute to the net acceleration. The precise strength of Earth's gravity varies depending on location. The nominal "average" value at the Earth's surface, known as standard gravity is, by definition, 9.80665 m/s2. This quantity is denoted variously as gn, ge, simply g. The Earth is not a perfect sphere, but is slightly flatter at the poles while bulging at the Equator: an oblate spheroid. There are consequently slight deviations in both the magnitude and direction of gravity across its surface. The net force as measured by a bob is called "effective gravity" or "apparent gravity". Effective gravity includes other factors that affect the net force. These factors include things such as centrifugal force at the surface from the gravitational pull of the Moon and Sun. In large cities, it ranges from 9.766 in Kuala Lumpur, Mexico City, Singapore to 9.825 in Oslo and Helsinki. The surface of the Earth is rotating, so it is not an inertial frame of reference. At latitudes nearer the Equator, the outward centrifugal force produced by Earth's rotation is larger than at polar latitudes. The same two factors influence the direction of the effective gravity.
Earth's gravity
–
Earth's gravity measured by NASA's GRACE mission, showing deviations from the theoretical gravity of an idealized smooth Earth, the so-called earth ellipsoid. Red shows the areas where gravity is stronger than the smooth, standard value, and blue reveals areas where gravity is weaker. (Animated version.)
Earth's gravity
–
Earth's radial density distribution according to the Preliminary Reference Earth Model (PREM).
128.
Proper acceleration
–
In relativity theory, proper acceleration is the physical acceleration experienced by an object. It is thus acceleration relative to a inertial, observer, momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from. A corollary is that all inertial observers always have a proper acceleration of zero. Proper acceleration contrasts with coordinate acceleration, dependent on choice of coordinate systems and thus upon choice of observers. For unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time. Thus the concept is useful: with accelerated coordinate systems, in curved spacetime. If the observer allowed to free-fall, the observer will experience coordinate acceleration, but no proper acceleration, thus no g-force. Generally, objects including objects in orbit, experience no proper acceleration. This state is also known as "zero gravity," or "free-fall," and it always produces a sensation of weightlessness. Only in such situations is coordinate acceleration entirely felt as a "g-force". As seen above, the proper force is equal to the opposing force, measured as an object's "operational weight". Thus, the proper force on an object is always opposite to its measured weight. This cancels the radially outward geometric acceleration associated with your coordinate frame. This outward acceleration will become the coordinate acceleration when you let causing you to fly off along a zero proper-acceleration path.
Proper acceleration
–
Map & traveler views of one-gee proper-acceleration from rest for one year.
129.
Fermion
–
In particle physics, a fermion is any particle characterized by Fermi–Dirac statistics. These particles obey the Pauli principle. Fermions differ from bosons, which obey Bose–Einstein statistics. It can be a composite particle, such as the proton. According to the spin-statistics theorem in any reasonable relativistic quantum theory, particles with integer spin are bosons, while particles with half-integer spin are fermions. Besides this characteristic, fermions have another specific property: they possess conserved baryon or lepton quantum numbers. Therefore, what is usually referred to as the spin statistics relation is in fact a spin statistics-quantum relation. As a consequence of the Pauli principle, only one fermion can occupy a particular quantum state at any given time. If multiple fermions have the spatial probability distribution, then at least one property of each fermion, such as its spin, must be different. Weakly interacting fermions can also display bosonic behavior under extreme conditions. At low temperature fermions show superfluidity for charged particles. Composite fermions, such as neutrons, are the key building blocks of everyday matter. The Standard Model recognizes two types of elementary fermions: leptons. In all, the model distinguishes 24 different fermions. There are six leptons, along with the corresponding antiparticle of each of these.
Fermion
–
Enrico Fermi
Fermion
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Large Hadron Collider tunnel at CERN
130.
Force carrier
–
In particle physics, force carriers or messenger particles or intermediate particles are particles that give rise to forces between other particles. These particles are bundles of energy of a particular kind of field. There is one kind of field for every type of elementary particle. For instance, there is an electromagnetic field whose quanta are photons. Strong interactions are called gauge bosons. In particle physics, field theories such as the Standard Model describe nature in terms of fields. Each field has a complementary description as the set of particles of a particular type. The quantum excitations of the field can be interpreted as particles. The Standard Model contains the following particles, each of, an excitation of a particular field: excitations of the strong gauge field. W bosons, Z bosons, excitations of the electroweak gauge fields. Higgs bosons, excitations of one component of the Higgs field, which gives mass to fundamental particles. Several types of fermions, described as excitations of fermionic fields. In addition, composite particles such as mesons can be described as excitations of an effective field. When one particle scatters off another, altering its trajectory, there are two ways to think about the process. In the picture, we imagine that the field generated by one particle caused a force on the other.
Force carrier
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Large Hadron Collider tunnel at CERN
131.
Rest mass
–
In other reference frames, the energy of the system increases, but system momentum is subtracted from this, so that the invariant mass remains unchanged. Systems whose four-momentum is a null vector are referred to as massless. These do not appear to exist. Any time-like four-momentum possesses a frame where the momentum is zero, a center of momentum frame. In this case, mass is positive and is referred to as the rest mass. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. The same is true for massless particles in such system, which add invariant mass and also rest mass according to their energy. For an massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it. In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total energy divided by c2. Note that for reasons above, such a frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame exists. For example, invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, mass is in general not an additive quantity.
Rest mass
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Possible 4-momenta of particles. One has zero invariant mass, the other is massive
132.
Little group
–
Common examples of spaces that groups act on are sets, topological spaces. Actions of groups on vector spaces are called representations of the group. Some groups can be interpreted as acting on spaces in a canonical way. This action is not canonical. A common way of specifying non-canonical actions is to describe a homomorphism φ to the group of symmetries of a set X. The φ is also frequently called the "action" of G, since specifying φ is equivalent to specifying an action. If X has additional structure, then φ is only called an action if for each g ∈ G, the φ preserves the structure of X. The abstraction provided by group actions is a powerful one, because it allows geometrical ideas to be applied to more abstract objects. Many objects in mathematics have natural group actions defined on them. In particular, groups can act on other groups, or even on themselves. The group G is said to act on X. The set X is called a G-set. For a left action h acts first and is followed by g, while for a right action g acts first and is followed by h. Because of the formula −1 = h−1g−1, one can construct a left action from a right action by composing with the inverse operation of the group. Also, a right action of a group G on X is the same thing as a left action of its opposite group Gop on X.
Little group
–
Given an equilateral triangle, the counterclockwise rotation by 120° around the center of the triangle maps every vertex of the triangle to another one. The cyclic group C 3 consisting of the rotations by 0°, 120° and 240° acts on the set of the three vertices.
133.
Standard Model
–
The Standard Model of particle physics is a theory concerning the electromagnetic, weak, strong nuclear interactions, as well as classifying all the subatomic particles known. It was developed as a collaborative effort of scientists around the world. The current formulation was finalized upon experimental confirmation of the existence of quarks. Since then, discoveries of the top quark, the Higgs boson have given further credence to the Standard Model. Of its success in explaining a wide variety of experimental results, the Standard Model is sometimes regarded as the "theory of almost everything". It does not incorporate the full theory of gravitation as account for the accelerating expansion of the Universe. The model does not contain any dark matter particle that possesses all of the required properties deduced from observational cosmology. It also does not incorporate neutrino oscillations. The development of the Standard Model was driven by experimental particle physicists alike. The first step towards the Standard Model was Sheldon Glashow's discovery of a way to combine the electromagnetic and weak interactions. In 1967 Steven Weinberg and Abdus Salam incorporated the Higgs mechanism into Glashow's interaction, giving it its modern form. The Higgs mechanism is believed to give rise to the masses of all the elementary particles in the Standard Model. This includes the masses of the fermions, i.e. the quarks and leptons. The W± and Z0 bosons were discovered experimentally in 1983; and the ratio of their masses was found to be as the Standard Model predicted. At present, energy are best understood in terms of the kinematics and interactions of elementary particles.
Standard Model
–
Large Hadron Collider tunnel at CERN
Standard Model
–
The Standard Model of elementary particles (more schematic depiction), with the three generations of matter, gauge bosons in the fourth column, and the Higgs boson in the fifth.
134.
Field (physics)
–
In physics, a field is a physical quantity, typically a number or tensor, that has a value for each point in space and time. On a weather map, the surface wind velocity is described by assigning a vector to each point on a map. Each vector represents the direction of the movement of air at that point. When a test electric charge is placed in this electric field, the particle accelerates due to a force. This led physicists to consider electromagnetic fields to be a physical entity, making a supporting paradigm of the edifice of modern physics. In practice, the strength of most fields has been found to diminish to the point of being undetectable. One consequence is that the Earth's gravitational field quickly becomes undetectable on cosmic scales. In fact in this theory an representation of field is a field particle, namely a boson. To Isaac Newton his law of universal gravitation simply expressed the gravitational force that acted between any pair of massive objects. In the eighteenth century, a new quantity was devised to simplify the bookkeeping of all these gravitational forces. The development of the independent concept of a field truly began with the development of the theory of electromagnetism. The independent nature of the field became more apparent with James Clerk Maxwell's discovery that waves in these fields propagated at a finite speed. Maxwell, at first, did not adopt the modern concept of a field as fundamental quantity that could independently exist. Instead, he supposed that the electromagnetic field expressed the deformation of some underlying medium -- the luminiferous aether -- much like the tension in a membrane. If that were the case, the observed velocity of the electromagnetic waves should depend to the aether.
Field (physics)
–
Illustration of the electric field surrounding a positive (red) and a negative (blue) charge.
135.
Higgs field
–
The Higgs boson is an elementary particle in the Standard Model of particle physics. It is the quantum excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory first suspected to exist in the 1960s. Unlike other known fields such as the electromagnetic field, it has a non-zero constant value in vacuum. The existence of the Higgs field would also resolve several other long-standing puzzles, such as the reason for the weak force's extremely short range. Although it is hypothesised that the Higgs field permeates the entire Universe, evidence for its existence has been very difficult to obtain. In principle, the Higgs field can be detected through its excitations, manifested as Higgs particles, but these are extremely difficult to produce and detect. Since then, the particle has been shown to behave, interact, decay in many of the ways predicted by the Standard Model. It was also tentatively confirmed to have even parity and zero spin, two fundamental attributes of a Higgs boson. This appears to be the first elementary scalar particle discovered in nature. The Higgs boson is named after Peter Higgs, one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. On December 10, 2013, two of them, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction. Although Higgs's name has come to be associated with this theory, several researchers between about 1960 and 1972 independently developed different parts of it. In the Standard Model, the Higgs particle is a boson with no spin, electric charge, or colour charge. It is also very unstable, decaying into other particles almost immediately. It is a quantum excitation of one of the four components of the Higgs field.
Higgs field
–
Large Hadron Collider tunnel at CERN
Higgs field
–
Candidate Higgs boson events from collisions between protons in the LHC. The top event in the CMS experiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in the ATLAS experiment shows a decay into 4 muons (red tracks).
Higgs field
–
The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen, Englert, Brout. Right: Higgs.
Higgs field
136.
Observable universe
–
There are at least two trillion galaxies in the observable universe. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical volume centered on the observer. Every location in the Universe has its observable universe, which may not overlap with the one centered on Earth. The word observable used in this sense does not depend on whether modern technology actually permits detection of radiation from an object in this region. It simply indicates that it is possible in principle for light or other signals from the object to reach an observer on Earth. In practice, we can see light only from back as the time of photon decoupling in the recombination epoch. That is when particles were first able to emit photons that were not quickly re-absorbed by other particles. Before then, the Universe was filled with a plasma, opaque to photons. The detection of gravitational waves indicates there is now a possibility of detecting non-light signals from before the recombination epoch. These are the photons we detect today as cosmic radiation. However, with future technology, it may be possible to observe the still older relic neutrino background, or even more distant events via gravitational waves. In the future, light from distant galaxies will have had more time to travel, so additional regions will become observable. . This fact can be used to define a type of cosmic event horizon whose distance from the Earth changes over time.
Observable universe
–
Hubble Ultra-Deep Field image of a region of the observable universe (equivalent sky area size shown in bottom left corner), near the constellation Fornax. Each spot is a galaxy, consisting of billions of stars. The light from the smallest, most red-shifted galaxies originated nearly 14 billion years ago.
Observable universe
–
Visualization of the whole observable universe. The scale is such that the fine grains represent collections of large numbers of superclusters. The Virgo Supercluster – home of Milky Way – is marked at the center, but is too small to be seen.
Observable universe
–
An example of one of the most common misconceptions about the size of the observable universe. Despite the fact that the universe is 13.8 billion years old, the distance to the edge of the observable universe is not 13.8 billion light-years, because the universe is expanding. This plaque appears at the Rose Center for Earth and Space in New York City.
Observable universe
–
Image (computer simulated) of an area of space more than 50 million light years across, presenting a possible large-scale distribution of light sources in the universe - precise relative contributions of galaxies and quasars are unclear.
137.
Proton
–
Protons and neutrons, each with masses of approximately one atomic mass unit, are collectively referred to as "nucleons". One or more protons are present in the nucleus of every atom. They are a necessary part of the nucleus. The number of protons in the nucleus is referred to as the atomic number. Since each element has a unique number of protons, each element has its own atomic number. This name was given to the hydrogen nucleus by Ernest Rutherford in 1920. In previous years Rutherford had discovered that the nucleus could be extracted from the nuclei of nitrogen by collision. Protons were therefore a candidate to be a building block of nitrogen and all other heavier atomic nuclei. In the modern Standard Model of particle physics, like neutrons, the other nucleon, are composed of three quarks. The rest masses of quarks contribute about 1 % of a proton's mass, however. At sufficiently low temperatures, free protons will bind to electrons. However, they remain protons. A fast proton moving through matter will slow with electrons and nuclei until it is captured by the electron cloud of an atom. The result is a protonated atom, a chemical compound of hydrogen. Such "free hydrogen atoms" tend to react chemically with other types of atoms at sufficiently low energies.
Proton
–
Ernest Rutherford at the first Solvay Conference, 1911
Proton
–
The quark structure of the proton. The color assignment of individual quarks is arbitrary, but all three colors must be present. Forces between quarks are mediated by gluons.
138.
Albert Einstein
–
Albert Einstein was a German-born theoretical physicist. Einstein developed the general theory of one of the two pillars of modern physics. Einstein's work is also known on the philosophy of science. Einstein is best known in popular culture for his mass -- energy equivalence E = mc2. This led him to develop his special theory of relativity. Einstein continued to deal with problems of statistical mechanics and theory, which led to his explanations of particle theory and the motion of molecules. Einstein also investigated the thermal properties of light which laid the foundation of the theory of light. In 1917, he applied the general theory of relativity to model the large-scale structure of the universe. Einstein settled in the U.S. becoming an American citizen in 1940. This eventually led to what would become the Manhattan Project. He largely denounced the idea of using the newly discovered nuclear fission as a weapon. Later, with the British philosopher Bertrand Russell, he signed the Russell -- Einstein Manifesto, which highlighted the danger of nuclear weapons. He was affiliated with the Institute until his death in 1955. He published more than 300 scientific papers along over 150 non-scientific works. On 5 universities and archives announced the release of Einstein's papers, comprising more than 30,000 unique documents.
Albert Einstein
–
Albert Einstein in 1921
Albert Einstein
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Einstein at the age of 3 in 1882
Albert Einstein
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Albert Einstein in 1893 (age 14)
Albert Einstein
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Einstein's matriculation certificate at the age of 17, showing his final grades from the Argovian cantonal school (Aargauische Kantonsschule, on a scale of 1–6, with 6 being the highest possible mark)
139.
General theory of relativity
–
General relativity is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics. In particular, the curvature of spacetime is directly related to the momentum of whatever matter and radiation are present. The relation is specified by a system of partial differential equations. Examples of such differences include gravitational time dilation, gravitational lensing, the gravitational time delay. The predictions of general relativity have been confirmed to date. Although general relativity is not the only relativistic theory of gravity, it is the simplest theory, consistent with experimental data. Einstein's theory has astrophysical implications. General relativity also predicts the existence of gravitational waves, which have since been observed directly by physics LIGO. In addition, general relativity is the basis of cosmological models of a consistently expanding universe. Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his relativistic framework. The Einstein field equations are very difficult to solve. Einstein used approximation methods in working out initial predictions of the theory. But early as 1916, the astrophysicist Karl Schwarzschild found the first non-trivial exact solution to the Einstein field equations, the Schwarzschild metric. The objects known today as black holes. In 1917, Einstein applied his theory as a whole initiating the field of relativistic cosmology.
General theory of relativity
–
A simulated black hole of 10 solar masses within the Milky Way, seen from a distance of 600 kilometers.
General theory of relativity
–
Albert Einstein developed the theories of special and general relativity. Picture from 1921.
General theory of relativity
–
Einstein cross: four images of the same astronomical object, produced by a gravitational lens
General theory of relativity
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Artist's impression of the space-borne gravitational wave detector LISA
140.
Weak equivalence principle
–
For Newton's equation of motion in a gravitational field, written out in full, it is: ⋅ = ⋅. It is only when there is numerical equality between the gravitational mass that the acceleration is independent of the nature of the body. This can be deduced without knowing in what manner gravity decreases with distance, but requires assuming the equivalency between gravity and inertia. The 1/54 ratio is Kepler's estimate of the Moon -- Earth ratio, based on their diameters. The accuracy of his statement can be deduced by using Galileo's gravitational observation that distance D = a t 2. Setting these accelerations equal for a mass is the equivalence principle. Einstein stated it thus: we assume a corresponding acceleration of the reference system. That is, being on the surface of the Earth is equivalent to being inside a spaceship, being accelerated by its engines. From this principle, Einstein deduced that free-fall is actually inertial motion. Objects in free-fall do not experience being accelerated downward but rather no acceleration. In an inertial frame of reference bodies obey Newton's first law, moving at constant velocity in straight lines. Analogously, in a curved spacetime the line of an inertial particle or pulse of light is as straight as possible. Such a line is called a geodesic and from the point of view of the inertial frame is a straight line. This is why an accelerometer in free-fall doesn't register any acceleration; there isn't any. This is possible because space is radically curved to a large gravitational mass.
Weak equivalence principle
–
General relativity
141.
Leaning Tower of Pisa
–
It is the third oldest structure in the city's Cathedral Square after the cathedral and the Pisa Baptistry. The tower's tilt began on one side to properly support the structure's weight. The height of the tower is 55.86 metres from 56.67 metres on the high side. The width of the walls at the base is 2.44 m. Its weight is estimated at 14,500 metric tons. The tower has 294 steps; the seventh floor has two fewer steps on the north-facing staircase. This means that the top of the tower is displaced 3.9 metres from the centre. There has been controversy about the real identity of the architect of the Leaning Tower of Pisa. Bonanno Pisano left Pisa for Monreale, Sicily, only to come back and die in his home town. Construction of the tower occurred over 199 years. Work on the floor of the white marble campanile began on August 14, 1173 during a period of military success and prosperity. This floor is a blind arcade articulated by engaged columns with classical Corinthian capitals. The tower began to sink after construction had progressed to the second floor in 1178. This was due to a three-metre foundation, set in weak, unstable subsoil, a design, flawed from the beginning. Construction was subsequently halted for almost a century, because the Republic of Pisa was almost continually engaged in battles with Genoa, Lucca, Florence.
Leaning Tower of Pisa
–
Leaning Tower of Pisa
Leaning Tower of Pisa
–
Pisa Cathedral & Leaning Tower of Pisa
Leaning Tower of Pisa
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Leaning Tower of Pisa in 2004
Leaning Tower of Pisa
142.
Inclined plane
–
The inclined plane is one of the six simple machines defined by Renaissance scientists. Moving an object up an inclined plane requires less force than lifting it up at a cost of an increase in the distance moved. This angle is equal to the arctangent of the coefficient of static μs between the surfaces. Two simple machines are often considered to be derived from the inclined plane. The wedge can be considered two inclined planes connected at the base. The screw consists of a inclined plane wrapped around a cylinder. The term may also refer to a specific implementation; a straight ramp cut for transporting goods up and down the hill. Inclined pulled up by a cable system; a funicular or cable railway, such as the Johnstown Inclined Plane. Inclined planes are widely used in the form of loading ramps to unload goods on trucks, ships, planes. Wheelchair ramps are used to allow people in wheelchairs to get over vertical obstacles without exceeding their strength. Slanted conveyor belts are also forms of inclined plane. In a funicular or railway a railroad car is pulled up a steep inclined plane using cables. Aircraft evacuation slides allow people to safely reach the ground from the height of a passenger airliner. Other inclined planes are built into permanent structures. Similarly, pedestrian sidewalks have gentle ramps to limit their slope, to ensure that pedestrians can keep traction.
Inclined plane
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Wheelchair ramp, Hotel Montescot, Chartres, France
Inclined plane
–
Using ramps to load a car on a truck
Inclined plane
–
Loading a truck on a ship using a ramp
Inclined plane
–
Aircraft emergency evacuation slide
143.
Torsion balance
–
Torsion coefficient links here. A spring is a spring that works by torsion or twisting;, a flexible elastic object that stores mechanical energy when it is twisted. When it is twisted, it exerts a force in the opposite direction, proportional to the amount it is twisted. There are two types. A bar is a straight bar of metal or rubber, subjected to twisting about its axis by torque applied at its ends. This terminology can be confusing because in a helical spring the forces acting on the wire are actually bending stresses, not torsional stresses. It is analogous to the spring constant of a linear spring. The negative sign indicates that the direction of the torque is opposite to the direction of twist. Coiled torsion springs are often used to operate pop-up doors found on small consumer goods like digital cameras and compact disc players. It absorbs road shocks as the wheel goes over rough road surfaces, cushioning the ride for the passengers. Torsion-bar suspensions are used in modern cars and trucks, as well as military vehicles. The bar used in many vehicle suspension systems also uses the torsion spring principle. The pendulum used in torsion pendulum clocks is a wheel-shaped weight suspended from its center by a wire torsion spring. The weight rotates about the axis of the spring, twisting it, instead of swinging like an ordinary pendulum. The force of the spring reverses the direction of rotation, so the wheel oscillates forth, driven at the top by the clock's gears.
Torsion balance
–
A mousetrap powered by a helical torsion spring
144.
Air resistance
–
In fluid dynamics, drag is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between a fluid and a solid surface. Unlike other resistive forces, of velocity, drag forces depend on velocity. Drag force is proportional to the squared velocity for a turbulent flow. Even though the ultimate cause of a drag is viscous friction, the turbulent drag is independent of viscosity. Drag forces always decrease fluid velocity relative to the solid object in the fluid's path. In the case of viscous drag of fluid in a pipe, force on the immobile pipe decreases fluid velocity relative to the pipe. In physics of sports, the drag force is necessary to explain the performance of runners, particularly of sprinters. The phrase parasitic drag is mainly used in aerodynamics, since for lifting wings drag is compared to lift. For flow around bluff bodies, then the qualifier "parasitic" is meaningless. Skin friction and interference drag on bluff bodies are not coined as being elements of "parasitic drag", but directly as elements of drag. Drag depends on the size, shape, speed of the object. At low R e, C D is asymptotically proportional to R e 1, which means that the drag is proportional to the speed. At high R e, C D is less constant. The graph to the right shows how C D varies e for the case of a sphere.
Air resistance
–
The power curve: form and induced drag vs. airspeed
Air resistance
–
0%
145.
Vacuum
–
Vacuum is space void of matter. The word stems from the Latin adjective vacuus for "vacant" or "void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. In engineering and applied physics on the other hand, vacuum refers to any space in which the pressure is lower than atmospheric pressure. The Latin term in vacuo is used to describe an object, surrounded by a vacuum. The quality of a partial vacuum refers to how closely it approaches a perfect vacuum. Lower gas pressure means higher-quality vacuum. For example, a typical cleaner produces enough suction to reduce air pressure by around 20 %. Higher-quality vacuums are possible. Ultra-high vacuum chambers, common in chemistry, engineering, operate below one trillionth of atmospheric pressure, can reach around 100 particles/cm3. Outer space is an even higher-quality vacuum, on average. In the electromagnetism in the 19th century, vacuum was thought to be filled with a medium called aether. In modern particle physics, the state is considered the ground state of matter. Vacuum was not studied empirically until the 17th century. Other experimental techniques were developed as a result of his theories of atmospheric pressure.
Vacuum
–
Pump to demonstrate vacuum
Vacuum
–
A large vacuum chamber
Vacuum
–
The Crookes tube, used to discover and study cathode rays, was an evolution of the Geissler tube.
Vacuum
–
A glass McLeod gauge, drained of mercury
146.
David Scott
–
David Randolph "Dave" Scott, is an American engineer, retired U.S. Air Force officer, former test pilot, former NASA astronaut. Scott belonged to the third group of NASA astronauts, selected in October 1963. As an astronaut, he became the seventh person to walk on the Moon. Before becoming an astronaut, he joined the United States Air Force. Scott graduated from Aerospace Research Pilot School. More than 5,600 hours of logged flying time. During this mission, he became the last American to fly solo in Earth orbit. He attended The Western High School in Washington, D.C. graduating in June 1949. In D.C. Scott was an student, on the school swim team and the Ambassador Hotel AAU champion team as a record setter. Because of his high standing in the class, Scott was able to choose which branch of the military he would serve. He chose the Air Force because he wanted to fly jets. Scott was assigned to the 32d Tactical Fighter Squadron at Soesterberg Air Base, Netherlands, to July 1960. Upon completing this tour of duty, Scott returned to the United States at the Massachusetts Institute of Technology. Scott received both a Master of Science degree in Aeronautics/Astronautics and the degree of Engineer from MIT in 1962. Scott also received an Honorary Doctorate of Astronautical Science in 1971.
David Scott
–
David Randolph Scott
David Scott
–
Recovery of the Gemini 8 spacecraft from the western Pacific Ocean
David Scott
–
Scott stands in the open hatch of the Apollo 9 Command Module Gumdrop
David Scott
–
One of the first day covers
147.
Apollo 15
–
Apollo 15 was the ninth manned mission in the United States' Apollo program, the fourth to land on the Moon, the eighth successful manned mission. It was also the first mission on which the Lunar Roving Vehicle was used. The mission ended on August 7. At the time, NASA called the most successful manned flight ever achieved. Commander David Scott and Lunar Module Pilot James Irwin spent three days including 18 1/2 hours outside the spacecraft on lunar extra-vehicular activity. The mission landed near Hadley rille, in an area of the Mare Imbrium called Palus Putredinus. They collected 77 kilograms of lunar material. Scott had left before graduating to accept an appointment to the United States Military Academy. The crewmen did their undergraduate work at either the United States Naval Academy. Originally Apollo 15 would have been an H mission, like Apollos 12, 14. But on September 1970, NASA announced it was canceling what were to be the current incarnations of the Apollo 15 and Apollo 19 missions. One of the major changes in the training for Apollo 15 was the training. Although on previous flights the crews had been trained in geology, for the first time Apollo 15 would make it a high priority. Scott and Irwin would train with a Caltech geologist who on Earth was interested in the Precambrian. Silver had been suggested by Harrison Schmitt as an alternative to the classroom lecturers that NASA had previously used.
Apollo 15
–
Jim Irwin with the Lunar Roving Vehicle on the first lunar surface EVA of Apollo 15
Apollo 15
Apollo 15
–
Commander David Scott during geology training in New Mexico on March 19, 1971
Apollo 15
–
Apollo 15 launches on July 26, 1971
148.
Theoretical physics
–
Theoretical physics is a branch of physics which employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science depends in general on the interplay between experimental studies and theory. In some cases, theoretical physics adheres to standards of mathematical rigor while giving little weight to experiments and observations. Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation. A physical theory is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory similarly differs from a mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms. A physical theory involves one or more relationships between various measurable quantities. Theoretical physics consists of several different approaches. In this regard, theoretical particle physics forms a good example. For instance: "phenomenologists" might employ empirical formulas to agree with experimental results, often without deep physical understanding. Some attempt to create approximate theories, called effective theories, because fully developed theories may be regarded as unsolvable or too complicated. Other theorists may try to unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.
Theoretical physics
–
Visual representation of a Schwarzschild wormhole. Wormholes have never been observed, but they are predicted to exist through mathematical models and scientific theory.
149.
Gravitational interaction
–
Gravity, or gravitation, is a natural phenomenon by which all things with mass are brought toward one another, including planets, stars and galaxies. Since mass are equivalent, all forms of energy, including light, also cause gravitation and are under the influence of it. On Earth, gravity causes the ocean tides. Gravity has an infinite range, although its effects become increasingly weaker on farther objects. The most extreme example of this curvature of spacetime is a black hole, from which nothing can escape once past its horizon, not even light. More gravity results in gravitational time dilation, where time lapses more slowly at a lower gravitational potential. Gravity is the weakest of the four fundamental interactions of nature. As a consequence, gravity plays no role in determining the internal properties of everyday matter. On the other hand, gravity is the cause of the formation, shape and trajectory of astronomical bodies. While the European thinkers are rightly credited with development of gravitational theory, there were pre-existing ideas which had identified the force of gravity. Later, the works of Brahmagupta referred to the presence of this force. Modern work on gravitational theory began in the late 16th and early 17th centuries. This was a major departure from Aristotle's belief that heavier objects have a higher gravitational acceleration. Galileo postulated resistance as the reason that objects with less mass may fall slower in an atmosphere. Galileo's work set the stage for the formulation of Newton's theory of gravity.
Gravitational interaction
–
Sir Isaac Newton, an English physicist who lived from 1642 to 1727
Gravitational interaction
–
Two-dimensional analogy of spacetime distortion generated by the mass of an object. Matter changes the geometry of spacetime, this (curved) geometry being interpreted as gravity. White lines do not represent the curvature of space but instead represent the coordinate system imposed on the curved spacetime, which would be rectilinear in a flat spacetime.
Gravitational interaction
–
Ball falling freely under gravity. See text for description.
Gravitational interaction
–
Gravity acts on stars that conform our Milky Way.
150.
Balance scales
–
Weighing scales are devices to measure weight or calculate mass. Balances are widely used in commerce, as many products are packaged by weight. Very accurate balances, called analytical balances are used in scientific fields such as chemistry. By the 1940s various electronic devices were being attached to these designs to make readings more accurate. A spring scale measures weight by reporting the distance that a spring deflects under a load. Spring scales force, the force of constraint acting on an object, opposing the local force of gravity. They are usually calibrated so that measured force translates to mass at earth's gravity. The object to be weighed can be set on a pivot and platform. In a scale, the spring either compresses. By Hooke's law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Pinion mechanisms are often used to convert the linear motion to a dial reading. With proper manufacturing and setup, however, spring scales can be rated as legal for commerce. To remove the error, a commerce-legal scale must either have temperature-compensated springs or be used at a fairly constant temperature. To eliminate the effect of gravity variations, a commerce-legal spring scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use hydraulic force to sense weight.
Balance scales
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Digital kitchen scale, a strain gauge scale
Balance scales
–
Scales used for trade purposes in the state of Florida, as this scale at the checkout in a cafeteria, are inspected for accuracy by the FDACS's Bureau of Weights and Measures.
Balance scales
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A two-pan balance
Balance scales
–
Two 10- decagram masses
151.
Nineteenth dynasty of Egypt
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The Nineteenth Dynasty of ancient Egypt was one of the periods of the Egyptian New Kingdom. Founded by Vizier Ramesses I, whom Pharaoh Horemheb chose as his successor to the throne, this dynasty is best known for its military conquests in Canaan. The warrior kings of the early 18th Dynasty had encountered only little resistance from neighbouring kingdoms, allowing them to expand their realm of influence easily. The situation had changed radically towards the end of the 18th Dynasty. The Pharaohs of the 19th dynasty ruled for approximately one ten years: to 1187 BC. Consequently, it will be amended to 11 years or 1290-1279 BC. Therefore, Seti's father and predecessor would have ruled Egypt between 1292-1290 BC. Many of the pharaohs were buried in the Valley of the Kings in Thebes. More information can be found on the Theban Mapping Project website. New Kingdom Egypt reached the zenith of its power under Seti I and Ramesses II, who campaigned vigorously against the Libyans and the Hittites. He ultimately accepted that a campaign against the Hittites was an unsupportable drain on Egypt's treasury and military. In his 21st regnal Ramesses signed the recorded peace treaty with Urhi-Teshub's successor, Hattusili III, with that act Egypt-Hittite relations improved significantly. Ramesses II even married two Hittite princesses, the first after his second Sed Festival. At least as early as Josephus, it was believed that Moses lived during the reign of Ramesses II. This dynasty declined as internal fighting between the heirs of Merneptah for the throne increased.
Nineteenth dynasty of Egypt
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Seti I
Nineteenth dynasty of Egypt
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Egyptian and Hittite Empires, around the time of the Battle of Kadesh (1274 BC).
Nineteenth dynasty of Egypt
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Ramesses II
Nineteenth dynasty of Egypt
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Seti II
152.
Anubis
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Like many ancient Egyptian deities, Anubis assumed different roles in various contexts. Depicted as a protector of graves early as the First Dynasty, Anubis was also an embalmer. By the Middle Kingdom he was replaced as lord of the underworld. One of his prominent roles was as a god who ushered souls into the afterlife. Anubis was depicted in a color that symbolized both rebirth and the discoloration of the corpse after embalming. Anubis is associated with Wepwawet, another Egyptian god with grey or white fur. Historians assume that the two figures were eventually combined. Anubis' female counterpart is Anput. His daughter is the serpent Kebechet. "Anubis" is a Greek rendering of this god's Egyptian name. In Egypt's Early Dynastic period, Anubis was portrayed with a "jackal" head and body. A "jackal" god, probably Anubis, is depicted from the reigns of Hor-Aha, Djer, other pharaohs of the First Dynasty. The oldest known textual mention of Anubis is in the Pyramid Texts of the Old Kingdom, where he is associated with the burial of the pharaoh. In the Old Kingdom, Anubis was the most important god of the dead. He was replaced in that role during the Middle Kingdom.
Anubis
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Anubis attending the mummy of the deceased.
Anubis
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Statue of Hermanubis, a hybrid of Anubis and the Greek god Hermes (Vatican Museums)
Anubis
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The "weighing of the heart," from the book of the dead of Hunefer. Anubis is portrayed as both guiding the deceased forward and manipulating the scales, under the scrutiny of the ibis-headed Thoth.
Anubis
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A crouching or "recumbent" statue of Anubis as a black-coated wolf (from the Tomb of Tutankhamun)
153.
Prehistoric numerals
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Counting in prehistory was first assisted by using body parts, primarily the fingers. Early systems of counting using tally marks appear in the Upper Paleolithic. The first more complex systems develop in the Ancient Near East together with the development of early writing out of proto-writing systems. Numerals originally developed with the oldest examples being about 35,000 to 25,000 years old. Counting aids like tally marks become developing into various types of proto-writing. The Cuneiform script develops out of proto-writing associated with keeping track of goods during the Chalcolithic. The Moksha people, whose existence dates to about the beginning of the 1st millennium BC, had a system. The numerals were tally marks carved on wood, drawn on clay or bark. In some places they were preserved mostly among small traders, bee-keepers, village elders. These numerals still can be found on old shepherd and tax-gatherer staffs, pottery. Http://www.thocp.net/timeline/0000.htm http://members.fortunecity.com/jonhays/tallying.htm
Prehistoric numerals
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Numeral systems
Prehistoric numerals
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Old Mokshan numerals
154.
Ratio
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In mathematics, a ratio is a relationship between two numbers indicating how many times the first number contains the second. For example, if a bowl of fruit contains six lemons, then the ratio of oranges to lemons is eight to six. Thus, a ratio can be a fraction as opposed to a whole number. Also, the ratio of oranges to the total amount of fruit is 8:14. The numbers compared in a ratio can be any quantities such as objects, persons, lengths, or spoonfuls. A ratio is written "a to b" or a:b, or sometimes expressed arithmetically as a quotient of the two. When the two quantities have the same units, as is often the case, their ratio is a dimensionless number. A rate is a quotient of variables having different units. But in many applications, the ratio is often used instead for this more general notion as well. B being the consequent. The proportion expressing the equality of the ratios A:B and C:D is written A:B = C:D or A:B::C:D. B and C are called the means. The equality of three or more proportions is called a continued proportion. Ratios are sometimes used with three or more terms. The ratio of the dimensions of a "two by four", ten inches long is 2:4:10.
Ratio
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The ratio of width to height of standard-definition television.
155.
Balance scale
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Weighing scales are devices to measure weight or calculate mass. Balances are widely used in commerce, as many products are sold and packaged by weight. Very accurate balances, called analytical balances are used in scientific fields such as chemistry. By the 1940s electronic devices were being attached to these designs to make readings more accurate. A scale measures weight by reporting the distance that a spring deflects under a load. Spring scales force, the tension force of constraint acting on an object, opposing the local force of gravity. They are usually calibrated so that measured force translates at earth's gravity. The object to be weighed can be set on a pivot and bearing platform. In a scale, the spring either stretches or compresses. By Hooke's law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Pinion mechanisms are often used to convert the linear spring motion to a dial reading. With proper setup, however, spring scales can be rated as legal for commerce. To remove the error, a commerce-legal spring scale must either have temperature-compensated springs or be used at a fairly constant temperature. To eliminate the effect of gravity variations, a commerce-legal scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use hydraulic force to weight.
Balance scale
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Digital kitchen scale, a strain gauge scale
Balance scale
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Scales used for trade purposes in the state of Florida, as this scale at the checkout in a cafeteria, are inspected for accuracy by the FDACS's Bureau of Weights and Measures.
Balance scale
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A two-pan balance
Balance scale
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Two 10- decagram masses
156.
Carob
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It is widely cultivated as an ornamental tree in gardens. The dried pod is often ground to carob powder, used to replace cocoa powder. An alternative to chocolate bars, are often available in health-food stores. A unit of mass for gemstones, of purity for gold, takes its name, indirectly, from the Greek word for a carob seed, kerátion. The Ceratonia tree grows up to 15 m tall. The crown supported by a thick trunk with brown rough bark and sturdy branches. Leaves may or may not have a terminal leaflet. It is frost-tolerant to roughly 20 °F. Most carob trees are dioecious, some are hermaphrodite. The male trees do not produce fruit. The trees blossom in autumn. The fruit is a legume, that can be elongated, compressed, straight, or thickened at the sutures. The pods take a full year to ripen. The ripe pods eventually fall to the ground and are eaten by various mammals, thereby dispersing the hard seed. The seeds contain a colourless chemical compound.
Carob
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Carob tree alfarroba χαρουπιά, ξυλοκερατιά keçiboynuzu
Carob
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Carob tree in Sardinia, Italy
Carob
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Ceratonia siliqua, ripe carob fruit pods
Carob
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Chocolate chip cookies with carob powder instead of cocoa powder
157.
Siliqua
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The siliqua is the modern name given to small, thin, Roman silver coins produced in the 4th century A.D. and later. When the coins were in circulation, the Latin siliqua was a unit of weight defined as one twenty-fourth of the weight of a Roman solidus. "Siliqua quarta pars solidi est, ab arbore, cuius semen est, vocabulum tenens." The name is taken from the seed of a tree. Since gold was worth about 14 times as much as silver in ancient Rome, such a silver coin would have a theoretical weight of 2.7 grams. There is historical evidence to support this premise. The term is one of convenience, as no name for these coins is indicated by contemporary sources. Thin silver coins to the 7th century which weigh about 2 to 3 grams are known by numismatic convention. The majority of examples suffer extensive clipping, thus to find both an untouched and undamaged example is fairly uncommon. A hoard of 14,212 silver siliquae dating from the early 5th century.
Siliqua
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Jovian siliqua, c. 363
Siliqua
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Constantine III (usurper)
158.
Ancient Roman units of measurement
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The ancient Roman units of measurement were largely built on the Hellenic system, which in turn was built upon Egyptian and Mesopotamian influences. The Roman units were well documented. The basic unit of Roman linear measurement was Roman foot. Investigation of its relation to the English foot goes back at least to 1647, when John Greaves published his Discourse on the Romane foot. An accepted modern value is 296 mm. The Roman foot was sub-divided either like the Greek pous into fingers; or into 12 unciae or inches. Frontinus writes in the 1st AD that the digitus was used in Campania and most parts of Italy. As no two surviving examples are identical, scholarly opinion ranges from 530 ml to ml. Cardarelli gives 549.28 ml. A 1952 estimate for its value in Pliny the Elder's Natural History estimated it as 500 ml. Modern estimates of the range from 322 to 329 g with 5076 grains or 328.9 g an accepted figure. The divisions of the libra were: The subdivisions of the uncia were: The complicated Roman calendar was replaced in 45 BC. In the Julian calendar, a leap year is 366 days long. Between AD 1, leap years occurred at irregular intervals. Starting in AD 4, leap years occurred regularly every four years.
Ancient Roman units of measurement
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Bronze modius measure (4th century AD) with inscription acknowledging Imperial regulation of weights and measures
159.
Kepler's laws of planetary motion
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In astronomy, Kepler's laws of planetary motion are three scientific laws describing the motion of planets around the Sun. The orbit of a planet is an ellipse with the Sun at one of the two foci. A line segment joining a planet and the Sun sweeps out equal areas during equal intervals of time. The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Most planetary orbits are nearly circular, careful observation and calculation are required in order to establish that they are not perfectly circular. Calculations of the orbit of Mars, whose published values are somewhat suspect, indicated an elliptical orbit. From this, Johannes Kepler inferred that other bodies in the Solar System, including those farther away from the Sun, also have elliptical orbits. Kepler's work improved the heliocentric theory of Nicolaus Copernicus, explaining how the planets' speeds varied, using elliptical orbits rather than circular orbits with epicycles. Kepler's laws are part of the foundation of modern astronomy and physics. Kepler's laws improve the model of Copernicus. Kepler's corrections are not at all obvious: The planetary orbit is not a circle, but an ellipse. The Sun is not at the center but at a focal point of the elliptical orbit. Neither the linear speed nor the angular speed of the planet in the orbit is constant, but the area speed is constant. The calculation is correct when perihelion, the date the Earth is closest to the Sun, falls on a solstice. The current perihelion, near January 4, is fairly close to the solstice of December 21 or 22.
Kepler's laws of planetary motion
160.
Tycho Brahe
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Tycho Brahe, born Tyge Ottesen Brahe, was a Danish nobleman known for his accurate and comprehensive astronomical and planetary observations. He was born in the then Danish peninsula of Scania. His observations were some five times more accurate than the best available observations at the time. An heir to several of Denmark's principal noble families, he received a comprehensive education. He took an interest in astronomy and in the creation of more accurate instruments of measurement. His system correctly saw the Moon as orbiting Earth, the planets as orbiting the Sun, but erroneously considered the Sun to be orbiting the Earth. Furthermore, he was the last of the major naked eye astronomers, working without telescopes for his observations. In his De stella of 1573, he refuted the Aristotelian belief in an celestial realm. Using similar measurements he showed that comets were also not atmospheric phenomena, as previously thought, must pass through the supposedly immutable celestial spheres. On the island he founded manufactories, such as a paper mill, to provide material for printing his results. He built an observatory at Benátky nad Jizerou. Both of his grandfathers and all of his great grandfathers had served as members of the Danish king's Privy Council. Both parents are buried under the floor of Kågeröd Church, four kilometres east of Knutstorp. Tycho was born at his family's ancestral seat of Knutstorp Castle, about eight kilometres north of Svalöv in then Danish Scania. He was the oldest of 12 siblngs, 8 of whom lived to adulthood.
Tycho Brahe
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Brahe wearing the Order of the Elephant
Tycho Brahe
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Portrait of Tycho Brahe (1596) Skokloster Castle
Tycho Brahe
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An artificial nose of the kind Tycho wore. This particular example did not belong to Tycho.
Tycho Brahe
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Tycho Brahe's grave in Prague, new tomb stone from 1901
161.
Elliptical
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As such, it is a generalization of a circle, a special type of an ellipse having both focal points at the same location. Ellipses are the closed type of conic section: a curve resulting by a plane. Ellipses have many similarities of conic sections: hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder. This ratio is called the eccentricity of the ellipse. Ellipses are common in engineering. The same is true for moons orbiting planets and all other systems having two astronomical bodies. The shapes of stars are well described by ellipsoids. It is also the simplest figure formed when the vertical motions are sinusoids with the same frequency. A similar effect leads to elliptical polarization of light in optics. ἔλλειψις, was given in his Conics emphasizing the connection of the curve with "application of areas". Ellipses have two perpendicular axes about which the ellipse is symmetric. Due to this symmetry, these axes intersect at the center of the ellipse. The larger of these two axes, which corresponds to the larger distance between antipodal points on the ellipse, is called the major axis. The smaller of these two axes, the smaller distance between antipodal points on the ellipse, is called the minor axis.
Elliptical
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Drawing an ellipse with two pins, a loop, and a pen
Elliptical
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An ellipse obtained as the intersection of a cone with an inclined plane.
162.
Square (algebra)
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In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. The adjective which corresponds to squaring is quadratic. The square of an integer may also be called a perfect square. In algebra, the operation of squaring is often generalized in systems of mathematical values other than the numbers. For instance, the square of the polynomial x + 1 is the quadratic polynomial x2 + 2x + 1. That is, the square function satisfies the identity x2 = 2. This can also be expressed by saying that the squaring function is an even function. The squaring function preserves the order of positive numbers: larger numbers have larger squares. In other words, squaring is a monotonic function on the interval. Hence, zero is its global minimum. This implies that the square of an integer is never less than the original number. Every real number is the square of exactly two numbers, one of, strictly positive and the other of, strictly negative. Zero is the square of only one number, itself. No square root can be taken within the system of real numbers because squares of all real numbers are non-negative.
Square (algebra)
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The composition of the tiling Image:ConformId.jpg (understood as a function on the complex plane) with the complex square function
Square (algebra)
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5⋅5, or 5 2 (5 squared), can be shown graphically using a square. Each block represents one unit, 1⋅1, and the entire square represents 5⋅5, or the area of the square.
163.
Cube (arithmetic)
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It is also the number multiplied by its square: n3 = n × n2. This is also the formula for a geometric cube with sides of n, giving rise to the name. The inverse operation of finding a number whose cube is n is called extracting the cube root of n. It determines the side of the cube of a given volume. It is also n raised to the one-third power. Both root are odd functions: 3 = −. The cube of any mathematical expression is denoted by a superscript 3, for example 23 = 8 or 3. A cube number, or just a cube, is a number, the cube of an integer. The difference between the cubes of consecutive integers can be expressed as follows: n3 − 3 = 3n + 1. Or 3 − n3 = 3n + 1. There is no minimum perfect cube, since the cube of a negative integer is negative. For example, 4 × − 4 × 4 = − 64. Unlike perfect squares, perfect cubes do not have a small number of possibilities for the last two digits. With even cubes, there is considerable restriction, for only 00, o2, e8 can be the last two digits of a perfect cube. Some cube numbers are also square numbers; for example, 64 is a number.
Cube (arithmetic)
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y = x 3 for values of 0 ≤ x ≤ 25.
164.
Semi-major axis
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The semi-major axis thus runs from the centre, to the perimeter. Essentially, it is the radius of an orbit at the orbit's two most distant points. For the special case of a circle, the semi-major axis is the radius. One can think of the semi-major axis as an ellipse's long radius. The semi-major axis of a hyperbola is, depending on the convention, plus or minus one half of the distance between the two branches. Thus it is the distance from the center to either vertex of the hyperbola. Thus a and b tend to infinity, a faster than b. In astronomy these extreme points are called apsis. A = r max + r min 2. The semi-minor axis of an ellipse is the geometric mean of these distances: b = r min. The eccentricity of an ellipse is defined as e = 1 − b 2 a 2 so r min = a, r max = a. Now consider the equation in polar coordinates, with r = ℓ. The semi-minor axis of an ellipse runs from the center of the ellipse to the edge of the ellipse. The semi-minor axis is half of the minor axis. The minor axis is the longest perpendicular to the major axis that connects two points on the ellipse's edge.
Semi-major axis
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The semi-major and semi-minor axis of an ellipse
165.
Solar System
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The Solar System is the gravitationally bound system comprising the Sun and the objects that orbit it, either directly or indirectly. Of the objects that orbit the Sun indirectly, the moons, two are larger than Mercury. The Solar System formed billion years ago from the gravitational collapse of a giant interstellar molecular cloud. The vast majority of the system's mass is with most of the remaining mass contained in Jupiter. Mercury, Venus, Earth and Mars, are terrestrial planets, being primarily composed of rock and metal. The four outer planets are giant planets, being substantially more massive than the terrestrials. All planets have almost circular orbits that lie within a nearly flat disc called the ecliptic. The Solar System also contains smaller objects. The asteroid belt, which lies between the orbits of Mars and Jupiter, mostly contains objects composed, of rock and metal. Within these populations are several dozen to possibly tens of thousands of objects large enough that they have been rounded by their own gravity. Such objects are categorized as dwarf planets. Identified dwarf planets include Pluto and Eris. In addition to these two regions, various small-body populations, including comets, centaurs and interplanetary dust clouds, freely travel between regions. Each of the outer planets is encircled by planetary rings of dust and small objects. A stream of charged particles flowing outwards from the Sun, creates a bubble-like region in the interstellar medium known as the heliosphere.
Solar System
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The Sun and planets of the Solar System (distances not to scale)
Solar System
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Solar System
Solar System
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Andreas Cellarius 's illustration of the Copernican system, from the Harmonia Macrocosmica (1660)
Solar System
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The eight planets of the Solar System (by decreasing size) are Jupiter, Saturn, Uranus, Neptune, Earth, Venus, Mars and Mercury.
166.
Galilean moons
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The Galilean moons are the four largest moons of Jupiter—Io, Europa, Ganymede, Callisto. They were discovered by Galileo Galilei around January 1610 and were the first group of objects found to orbit another planet. Their names derive from the lovers of Zeus. Ganymede is the largest moon in the Solar System, is even bigger than the planet Mercury. The three inner moons -- Ganymede -- are in a 4:2:1 orbital resonance with each other. Galileo initially named his discovery the Cosmica Sidera, but the names that eventually prevailed were chosen by Simon Marius. This allowed Galilei to discover in either December 1609 or January 1610 what came to be known as the Galilean moons. On January 7, 1610, Galileo wrote a letter containing the first mention of Jupiter's moons. At the time, he saw only three of them, he believed them to be fixed stars near Jupiter. He continued to observe these celestial orbs to March 1610. In these observations, he discovered a fourth body, also observed that the four were not fixed stars, but rather were orbiting Jupiter. Nevertheless, Galileo accepted the Copernican theory. In 1605, Galileo had been employed as a mathematics tutor for Cosimo de' Medici. In 1609, Cosimo became Grand Duke Cosimo II of Tuscany. Galileo, seeking patronage from his now-wealthy former student and his powerful family, used the discovery of Jupiter's moons to gain it.
Galilean moons
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Montage of Jupiter 's four Galilean moons, in a composite image comparing their sizes and the size of Jupiter. From top to bottom: Io, Europa, Ganymede, Callisto.
Galilean moons
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Galileo Galilei, the discoverer of the four moons
Galilean moons
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The Medician stars in the Sidereus Nuncius (the 'starry messenger'), 1610. The moons are drawn in changing positions.
Galilean moons
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A Jovilabe: an apparatus from the mid-18th century for demonstrating the orbits of Jupiter's satellites
167.
Vincenzo Viviani
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Vincenzo Viviani was an Italian mathematician and scientist. He was a disciple of Galileo. Raised in Florence, Viviani studied at a Jesuit school. Grand Duke Ferdinando II de' Medici furnished him a scholarship to purchase mathematical books. He worked on physics and geometry. At the age of 17, he was an assistant of Galileo Galilei in Arcetri. He remained a disciple in 1642. From 1655 to 1656, Viviani edited the first edition of Galileo's collected works. After Torricelli's 1647 death, Viviani was appointed to fill his position in Florence. Viviani was also one of the first members of the Accademia del Cimento, when it was created a decade later. In 1660, Giovanni Alfonso Borelli conducted an experiment to determine the speed of sound. The currently accepted value is 331.29 m/s at 0 ° C or 340.29 m/s at level. It has also been claimed that in 1661 he experimented with the rotation of pendulums, 190 years by Foucault. By 1666, Viviani started to receive many job offers as his reputation as a mathematician grew. Fearful of losing Viviani, the Grand Duke appointed court mathematician.
Vincenzo Viviani
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Vincenzo Viviani
Vincenzo Viviani
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The "Palazzo Viviani" or "Palazzo dei Cartelloni" with plaques and bust dedicated by Viviani to Galilei
168.
Ball
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A ball is a round object with various uses. Balls can also be used for simpler activities, such as catch, marbles and juggling. Balls made from hard-wearing materials are used in engineering applications to provide very low friction bearings, known as ball bearings. Black-powder weapons use metal balls as projectiles. Although many types of balls are today made from rubber, this form was unknown outside the Americas after the voyages of Columbus. The Spanish were the first Europeans to see bouncing rubber balls which were employed most notably in the Mesoamerican ballgame. No Old English representative of any of these is known. If ball - was native in Germanic, it may have been a cognate with the Latin foll-is in sense of a "thing inflated." French balle is assumed to be of itself, however. In Ancient Greek the πάλλα for "ball" is attested besides the word" σφαίρα", sphere. A ball, as the essential feature in many forms of gameplay requiring physical exertion, must date from the very earliest times. A rolling object appeals not only to a kitten and a puppy. Some form of game with a ball is played among aboriginal tribes at the present day. In Homer, Nausicaa was playing at ball with her maidens when Odysseus first saw her in the land of the Phaeacians. And Halios and Laodamas performed with ball play, accompanied with dancing.
Ball
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Russian leather balls (Russian: мячи), 12th-13th century.
Ball
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Football from association football (soccer)
Ball
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Baoding balls
Ball
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Baseball
169.
Groove (engineering)
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Examples include: A canal cut in a hard material, usually metal. This canal can be round, an arc in order to receive another component such as a boss, a tongue or a gasket. It can also be on the circumference of a dowel, an axle or on the outside or inside of a tube or pipe etc.. This canal may receive an o-ring or a gasket. A depression on the entire circumference of a cast or machined wheel, a pulley or sheave. This depression may receive a cable, a belt. A longitudinal channel formed in a hot rolled profile such as a grooved rail. This groove is for the flange on a wheel.
Groove (engineering)
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v
170.
Parchment
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Parchment is a material made from processed animal skin and used—mainly in the past—for writing on. Parchment is most commonly made of calfskin, goatskin. It was historically used for writing documents, the pages of a book. Parchment is limed, dried under tension. It is thus different from leather. It may be called animal membrane by museums that wish to avoid distinguishing between "parchment" and the more restricted term "vellum". The term "parchment" originally referred only to the skin of sheep and, occasionally, goats. The parchment evolved from the name of the city of Pergamon, a thriving center of parchment production during the Hellenistic period. This however is a myth; parchment had elsewhere long before the rise of Pergamon. In the 2nd BC a great library was set up in Pergamon that rivaled the famous Library of Alexandria. Writing on prepared animal skins had a long history, however. Though the Babylonians impressed their cuneiform on clay tablets, they also wrote on parchment from the 6th century BC onward. Early Islamic texts are also found on parchment. New techniques in milling allowed it to be much cheaper than parchment; it was still made of textile rags and of very high quality. With the advent of printing in the later century, the demands of printers far exceeded the supply of animal skins for parchment.
Parchment
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Central European (Northern) type of finished parchment made of goatskin stretched on a wooden frame
Parchment
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Latin Grant written on fine parchment or vellum with seal dated 1329
Parchment
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A 1385 copy of the Sachsenspiegel, a German legal code, written on parchment with straps and clasps on the binding
Parchment
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A Sefer Torah, the traditional form of the Hebrew Bible, is a scroll of parchment.
171.
Angle
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This plane does not have to be a Euclidean plane. Angles are also formed by the intersection of two planes in other spaces. These are called dihedral angles. Angles formed by the intersection of two curves in a plane are defined as the angle determined at the point of intersection. Angle is also used to designate the measure of an angle or of a rotation. This measure is the ratio of the length of a circular arc to its radius. In the case of a geometric angle, the arc is delimited by the sides. The angle comes from the Latin word angulus, meaning "corner"; cognate words are the Greek ἀγκύλος, meaning "crooked, curved," and the English word "ankle". Both are connected with * ank -, meaning "to bend" or "bow". According to Proclus an angle must be a relationship. In mathematical expressions, it is common to use Greek letters to serve as variables standing for the size of some angle. Lower Roman letters are also used, as are upper case Roman letters in the context of polygons. See the figures in this article for examples. In geometric figures, angles may also be identified by the labels attached to the three points that define them. For example, the angle at vertex A enclosed by the rays AB and AC is denoted B A C ^.
Angle
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An angle enclosed by rays emanating from a vertex.
172.
Sidereal orbital period
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A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. It equals 365.25636 SI days for the J2000.0 epoch. The sidereal year differs in successive years due to the precession of the equinoxes. Before the discovery of the precession of the equinoxes by Hipparchus in the Hellenistic period, the difference between tropical year was unknown. Anomalistic year Gaussian year Orbital period Julian year Precession Sidereal time Tropical year
Sidereal orbital period
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Key concepts
173.
Astronomical unit
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The astronomical unit is a unit of length, roughly the distance from Earth to the Sun. However, that distance varies as Earth orbits a year. Originally conceived as the average of Earth's perihelion, it is now defined as exactly 7011149597870700000 ♠ 149597870700 metres. The astronomical unit is used primarily for measuring distances within the Solar System or around other stars. However, it is also a fundamental component in the definition of another unit of the parsec. A variety of unit abbreviations have been in use for the astronomical unit. In a 1976 resolution, the International Astronomical Union used the A for the astronomical unit. In 2006, the International Bureau of Measures recommended ua as the symbol for the unit. In 2012, the IAU, noting "that various symbols are presently in use for the astronomical unit", recommended the use of the symbol "au". In the 2014 revision of the SI Brochure, the BIPM used the symbol "au". In ISO 80000-3, the symbol of the astronomical unit is "ua". Earth's orbit around the Sun is an ellipse. The semi-major axis of this ellipse is defined to be half of the straight segment that joins the aphelion and perihelion. The centre of the sun lies on this straight segment, but not at its midpoint. A star's shift enabled the star's distance to be calculated.
Astronomical unit
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Transits of Venus across the face of the Sun were, for a long time, the best method of measuring the astronomical unit, despite the difficulties (here, the so-called " black drop effect ") and the rarity of observations.
Astronomical unit
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The red line indicates the Earth-Sun distance, which is on average about 1 astronomical unit.
174.
Sidereal year
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A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed stars. It equals 365.25636 SI days for the J2000.0 epoch. The sidereal year differs from the tropical year, the time interval between vernal equinoxes in successive years, due to the precession of the equinoxes. Before the discovery of the precession of the equinoxes by Hipparchus in the Hellenistic period, the difference between sidereal and tropical year was unknown. Anomalistic year Gaussian year Orbital period Julian year Precession Sidereal time Tropical year
Sidereal year
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Key concepts
175.
Robert Hooke
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Robert Hooke FRS was an English natural philosopher, architect and polymath. These issues may have contributed to his historical obscurity. Allan Chapman has characterised him as "England's Leonardo". He studied at Oxford during the Protectorate where he became one of a tightly knit group of ardent Royalists led by John Wilkins. Hooke observed the rotations of Mars and Jupiter. In 1665 Hooke inspired the use of microscopes for scientific exploration with Micrographia. Based on his microscopic observations of fossils, he was an early proponent of biological evolution. Much of what is known of Hooke's early life comes from an autobiography that he commenced in 1696 but never completed. Richard Waller mentions it in his introduction to The Posthumous Works of M.D. S.R.S. printed in 1705. The work of Waller, along with John Ward's Lives of the Gresham Professors and John Aubrey's Brief Lives, form the major biographical accounts of Hooke. Robert Hooke was born in 1635 in Freshwater to John Hooke and Cecily Gyles. His two brothers were also ministers. Robert Hooke was expected to join the Church. Robert, too, grew up to be a staunch monarchist. As a youth, Robert Hooke was fascinated by observation, drawing, interests that he would pursue in various ways throughout his life.
Robert Hooke
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Modern portrait of Robert Hooke (Rita Greer 2004), based on descriptions by Aubrey and Waller; no contemporary depictions of Hooke are known to survive.
Robert Hooke
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Memorial portrait of Robert Hooke at Alum Bay, Isle of Wight, his birthplace, by Rita Greer (2012).
Robert Hooke
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Robert Boyle
Robert Hooke
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Diagram of a louse from Hooke's Micrographia
176.
Celestial bodies
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An astronomical object or celestial object is a naturally occurring physical entity, association, or structure that current science has demonstrated to exist in the observable universe. In astronomy, the terms "object" and "body" are often used interchangeably. Examples for astronomical objects include planetary systems, galaxies, while asteroids, moons, planets, stars are astronomical bodies. The universe can be viewed as having a hierarchical structure. At the largest scales, the fundamental component of assembly is the galaxy. Disc galaxies encompass spiral galaxies with features, such as a distinct halo. At the core, most galaxies have a black hole, which may result in an galactic nucleus. Galaxies can also have satellites in the form of dwarf galaxies and globular clusters. The constituents of a galaxy are formed out of gaseous matter that assembles through gravitational self-attraction in a hierarchical manner. At this level, the resulting fundamental components are the stars, which are typically assembled in clusters from the various condensing nebulae. The great variety of stellar forms are determined entirely by the mass, evolutionary state of these stars. Stars may be found in multi-star systems that orbit about each other in a hierarchical organization. The distinctive types of stars are shown by the Hertzsprung -- Russell diagram -- a plot of stellar luminosity versus surface temperature. Each star follows an evolutionary track across this diagram. If this track takes the star through a region containing an intrinsic variable type, then its physical properties can cause it to become a variable star.
Celestial bodies
Celestial bodies
Celestial bodies
Celestial bodies
177.
Calculus
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It has two major branches, integral calculus; these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed by Isaac Newton and Gottfried Leibniz. Calculus has widespread uses in science, engineering and economics. Calculus is a part of modern education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". Calculus is also used for naming theories of computation, such as propositional calculus, calculus of variations, lambda calculus, process calculus. The method of exhaustion was later reinvented by Liu Hui in the 3rd century AD in order to find the area of a circle. In the 5th AD, Zu Chongzhi established a method that would later be called Cavalieri's principle to find the volume of a sphere. Indian mathematicians gave a semi-rigorous method of differentiation of some trigonometric functions. In the Middle East, Alhazen derived a formula for the sum of fourth powers. The infinitesimal quantities he introduced were disreputable at first. The formal study of calculus brought together Cavalieri's infinitesimals with the calculus of finite differences developed at around the same time. Pierre de Fermat, claiming that he borrowed from Diophantus, introduced the concept of adequality, which represented equality up to an infinitesimal term.
Calculus
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Isaac Newton developed the use of calculus in his laws of motion and gravitation.
Calculus
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Gottfried Wilhelm Leibniz was the first to publish his results on the development of calculus.
Calculus
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Maria Gaetana Agnesi
Calculus
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The logarithmic spiral of the Nautilus shell is a classical image used to depict the growth and change related to calculus
178.
Royal Society
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Founded in November 1660, it was granted a royal charter by King Charles II as "The Royal Society". The society is governed by its Council, chaired according to a set of statutes and standing orders. As of 2016, there are about 1,600 fellows, allowed to use the postnominal FRS, with up to 52 new fellows appointed each year. There are also royal fellows, foreign members, the last of which are allowed to use the postnominal title ForMemRS. The Royal Society President is Venkatraman Ramakrishnan, who took up the post on November 2015. The Royal Society started from groups of natural philosophers, meeting at variety of locations, including Gresham College in London. They were influenced by the "new science", as promoted from approximately 1645 onwards. A group known as "The Philosophical Society of Oxford" was run under a set of rules still retained by the Bodleian Library. After the English Restoration, there were regular meetings at Gresham College. It is widely held that these groups were the inspiration for the foundation of the Royal Society. I will not say, that Mr Oldenburg did rather inspire, at least, did help them, hinder us. Since then, every monarch has been the patron of the society. The society's early meetings included experiments performed first by Hooke and then by Denis Papin, appointed in 1684. These experiments were both important in some cases and trivial in others. The Society returned in 1673.
Royal Society
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The entrance to the Royal Society in Carlton House Terrace, London
Royal Society
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The President, Council, and Fellows of the Royal Society of London for Improving Natural Knowledge
Royal Society
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John Evelyn, who helped to found the Royal Society
Royal Society
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Mace granted by Charles II
179.
Escape velocity
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The escape velocity from Earth is about 11.186 km/s at the surface. More generally, velocity is the speed at which the sum of an object's kinetic energy and its gravitational potential energy is equal to zero. Given escape perpendicular to a massive body, the object will move away from the body, slowing forever and approaching but never reaching zero speed. Once velocity is achieved, no further impulse need be applied for it to continue in its escape. In these equations atmospheric friction is not taken into account. A barycentric velocity is a velocity of one body relative to the center of mass of a system of bodies. A relative velocity is the velocity of one body with respect to another. Relative velocity is defined only in systems with two bodies. In gravitational fields "velocity" refers to the escape velocity of zero mass test particles relative to the barycenter of the masses generating the field. The existence of velocity is a consequence of conservation of energy. The simplest way of deriving the formula for velocity is to use conservation of energy. Imagine that a spaceship of mass m is at a distance r from the center of mass of the planet, whose mass is M. Its initial speed is equal to its escape velocity, v e. At its final state, its speed will be negligibly small and assumed to be 0. All velocities measured with respect to the field.
Escape velocity
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Luna 1, launched in 1959, was the first man-made object to attain escape velocity from Earth (see below table).
Escape velocity
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General
180.
Newton's cannonball
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It appeared in his book A Treatise of the System of the World. In this experiment from his book, Newton visualizes a cannon on top of a very high mountain. If a gravitational force acts on the cannonball, it will follow a different path depending on its initial velocity. If the speed is low, it will simply fall back on Earth. For example horizontal speed of 0 to 7,000 m/s for Earth. An image of the page from the System of the World showing Newton's diagram of this experiment was included on the Voyager Golden Record.
Newton's cannonball
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Contents
181.
Thought experiment
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A thought experiment considers some hypothesis, theory, or principle for the purpose of thinking through its consequences. Perhaps the key experiment in the history of modern science is Galileo's demonstration that falling objects must fall at the same rate regardless of their masses. The'experiment' is described by Galileo in Discorsi e dimostrazioni matematiche thus: Salviati. Do you not agree with me in this opinion? Simplicio. You are unquestionably right. Salviati. Hence the heavier body moves with less speed than the lighter; an effect, contrary to your supposition. Instead, many philosophers prefer to consider'Thought Experiments' to be merely the use of a hypothetical scenario to help understand the way things actually are. Thought experiments have been used in a variety including philosophy, law, physics, mathematics. In philosophy, they have been used at least since some pre-dating Socrates. In law, they were well-known to Roman lawyers quoted in the Digest. Johann Witt-Hansen established that Hans Christian Ørsted was the first to use the Latin-German mixed term Gedankenexperiment 1812. Ørsted was also the first to use Gedankenversuch, in 1820. It first appeared in the 1897 English translation of one of Mach's papers.
Thought experiment
–
Temporal representation of a prefactual thought experiment.
Thought experiment
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A famous example, Schrödinger's cat (1935), presents a cat that might be alive or dead, depending on an earlier random event. It illustrates the problem of the Copenhagen interpretation applied to everyday objects.
Thought experiment
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Temporal representation of a counterfactual thought experiment.
Thought experiment
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Temporal representation of a semifactual thought experiment.
182.
Celestial spheres
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The celestial spheres, or celestial orbs, were the fundamental entities of the cosmological models developed by Plato, Eudoxus, Aristotle, Ptolemy, Copernicus and others. In modern thought, the orbits of the planets are viewed through mostly empty space. When scholars applied Ptolemy's epicycles, they presumed that each planetary sphere was exactly thick enough to accommodate them. In Greek antiquity the ideas of celestial rings first appeared in the cosmology of Anaximander in the early 6th century BC. All these wheel rims had originally been formed out of an original sphere of fire wholly encompassing the Earth, which had disintegrated into individual rings. As viewed from the Earth, the sphere of the stars was lowest. Following Anaximander, his pupil Anaximenes held that the stars, Sun, planets are all made of fire. And unlike Anaximander, he relegated the fixed stars from the Earth. After Anaximenes, Pythagoras, Xenophanes and Parmenides all held that the universe was spherical. But it posited that the planets were spherical bodies set in rings rather than wheel rims as in Anaximander's cosmology. Each planet is attached to the innermost of its particular set of spheres. In his Metaphysics, Aristotle developed a physical cosmology of spheres, based on the mathematical models of Eudoxus. Aristotle considers that these spheres are made of the aether. In more detailed models the seven planetary spheres contained secondary spheres within them. In antiquity the order of the lower planets was not universally agreed.
Celestial spheres
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The Earth within seven celestial spheres, from Bede, De natura rerum, late 11th century
Celestial spheres
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Geocentric celestial spheres; Peter Apian's Cosmographia (Antwerp, 1539)
Celestial spheres
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Thomas Digges' 1576 Copernican heliocentric model of the celestial orbs
Celestial spheres
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Kepler's diagram of the celestial spheres, and of the spaces between them, following the opinion of Copernicus (Mysterium Cosmographicum, 2nd ed., 1621)
183.
Unit conversion
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Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors. The process of conversion depends on the intended purpose. This may be governed by regulation, contract, other published standards. Engineering judgment may include such factors as: the associated uncertainty of measurement. The statistical confidence interval or tolerance interval of the initial measurement. The number of significant figures of the measurement. The intended use of the measurement including the engineering tolerances. Historical definitions of the units and their derivatives used in old measurements; e.g. international foot vs. US survey foot. Some conversions from one system of units to another need to be exact, without decreasing the precision of the first measurement. This is sometimes called soft conversion. It does not involve changing the physical configuration of the item being measured. By contrast, an adaptive conversion may not be exactly equivalent. It changes the measurement to convenient and workable units in the new system. It sometimes involves size substitution, of the item.
Unit conversion
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Base units
184.
Cavendish experiment
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Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the specific gravity of the Earth, or equivalently the mass of the Earth. His experiment gave the accurate values for these geophysical constants. The experiment was devised sometime by geologist John Michell, who constructed a torsion balance apparatus for it. However, Michell died without completing the work. Cavendish then reported his results in the Philosophical Transactions of the Royal Society in 1798. Two 348-pound lead balls were located near the smaller balls, about 9 inches away, held in place with a separate suspension system. The experiment measured the gravitational attraction between the small balls and the larger ones. The two large balls were positioned on alternate sides of the wooden arm of the balance. Their mutual attraction to the small balls caused the arm to rotate, twisting the wire supporting the arm. Cavendish found that the Earth's density was ♠ 5.448 ± 0.033 times that of water. The period was about 20 minutes. The coefficient could be calculated from this and the mass and dimensions of the balance. Actually, the rod was never at rest; Cavendish had to measure the angle of the rod while it was oscillating. Cavendish's equipment was remarkably sensitive for its time.
Cavendish experiment
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Detail showing torsion balance arm (m), large ball (W), small ball (x), and isolating box (ABCDE).
Cavendish experiment
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Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside. Figure 1 of Cavendish's paper.
185.
Weighing
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In science and engineering, the weight of an object is usually taken to be the force on the object due to gravity. The unit of measurement for weight is that of force, which in the International System of Units is the newton. In this sense of weight, a body can be weightless only if it is far away from any other mass. Although weight and mass are scientifically distinct quantities, the terms are often confused with each other in everyday use. There is also a rival tradition within Newtonian physics and engineering which sees weight as that, measured when one uses scales. There the weight is a measure of the magnitude of the reaction force exerted on a body. Thus, in a state of free fall, the weight would be zero. In this second sense of weight, terrestrial objects can be weightless. The famous apple falling on its way to meet the ground near Isaac Newton, is weightless. In the community, a considerable debate has existed over half a century on how to define weight for their students. The current situation is that a multiple set of concepts co-exist and find use in their various contexts. Discussion of the concepts of lightness date back to the Greek philosophers. These were typically viewed as inherent properties of objects. Plato described weight as the natural tendency of objects to seek their kin. To Aristotle weight and levity represented the tendency to restore the natural order of the basic elements: air, earth, fire and water.
Weighing
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Ancient Greek official bronze weights dating from around the 6th century BC, exhibited in the Ancient Agora Museum in Athens, housed in the Stoa of Attalus.
Weighing
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Weighing grain, from the Babur-namah
Weighing
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This top-fuel dragster can accelerate from zero to 160 kilometres per hour (99 mph) in 0.86 seconds. This is a horizontal acceleration of 5.3 g. Combined with the vertical g-force in the stationary case the Pythagorean theorem yields a g-force of 5.4 g. It is this g-force that causes the driver's weight if one uses the operational definition. If one uses the gravitational definition, the driver's weight is unchanged by the motion of the car.
Weighing
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Measuring weight versus mass
186.
Spring scales
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A spring scale or spring balance or Newton meter is a type of weighing scale. It consists of spring fixed at one end with a hook to attach an object at the other. Therefore the scale markings on the spring balance are equally spaced. A spring scale can not measure mass, only weight. Also, the spring in the scale can permanently stretch with repeated use. A spring scale will only read correctly in a frame of reference where the acceleration in the spring axis is constant. The scale on top would read slightly heavier due to also supporting the weight of the lower scale itself. Spring balances come in different sizes. The largest scale ranged from 5000-8000 newtons. A balance may be labeled in both units of mass. Strictly speaking, only the force values are correctly labeled. Material carried on a belt. They are also common in science education as basic accelerators. They are used when the accuracy afforded by other types of scales can be sacrificed for robustness. A spring balance measures the weight of an object by opposing the force of gravity acting with the force of an extended spring.
Spring scales
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Spring balance, measuring in gram.
Spring scales
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Example of spiral balancer for sash windows
187.
Spring (device)
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A spring is an elastic object used to store mechanical energy. Springs are usually made out of steel. There are a large number of spring designs; in everyday usage the term often refers to coil springs. When a spring is stretched from its resting position, it exerts an opposing force approximately proportional to its change in length. The rate or constant of a spring is the change in the force it exerts, divided by the change in deflection of the spring. That is, it is the gradient of the force versus curve. An extension or spring's rate is expressed in units of force divided by distance, for example lbf/in or N/m. A spring's rate is in units of torque divided by angle, such as N · m/rad or ft · lbf/degree. The inverse of rate is compliance,: if a spring has a rate of 10 N/mm, it has a compliance of 0.1 mm/N. The stiffness of springs in parallel is additive, as is the compliance of springs in series. Springs are made from a variety of the most common being spring steel. Small springs can be wound from pre-hardened stock, while larger ones are made after fabrication. Some non-ferrous metals are also used including phosphor titanium for parts requiring corrosion resistance and beryllium copper for springs carrying electrical current. Non-coiled springs were used throughout human history, e.g. the bow. In the Age more sophisticated spring devices were used, as shown by the spread of tweezers in many cultures.
Spring (device)
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Helical or coil springs designed for tension.
Spring (device)
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A heavy-duty helical spring designed for compression and tension.
Spring (device)
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The English longbow – a simple but very powerful spring made of yew, measuring 2 m (6 ft 6 in) long, with a 470 N (105 lbf) draw force
Spring (device)
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A machined spring incorporates several features into one piece of bar stock
188.
Hooke's law
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The law is named after 17th-century British physicist Robert Hooke. He first stated the law in 1660 as a Latin anagram. He published the solution of his anagram in 1678 as: ut tensio, sic vis. An elastic body or material for which this equation can be assumed is said to be linear-elastic or Hookean. Hooke's law is only a linear approximation to applied forces. Many materials will noticeably deviate from Hooke's law well before those elastic limits are reached. On the other hand, Hooke's law is an accurate approximation for most solid bodies, long as the deformations are small enough. It is also the fundamental principle behind the balance wheel of the mechanical clock. Suppose that the spring has reached a state of equilibrium, where its length is not changing anymore. Let X be the amount by which the free end of the spring was displaced from its "relaxed" position. Hooke's law states that F = k X or, equivalently, X = k where k is characteristic of the spring. Moreover, the same formula holds when the spring is compressed, with F and X both negative in that case. In that case, the equation becomes F = − k X since the direction of the restoring force is opposite to that of the displacement. The displacement X in this case is the deviation of the beam, measured in the transversal direction, relative to its unloaded shape. The law also applies when a stretched steel wire is twisted by pulling on a lever attached to one end.
Hooke's law
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Hooke's law: the force is proportional to the extension
189.
Calibration
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Strictly, the term calibration means just the act of comparison, does not include any subsequent adjustment. The calibration standard is normally traceable to a national standard held by a National Metrological Institute. The increasing need for known accuracy and uncertainty and the need to have consistent and comparable standards internationally has led to the establishment of National laboratories. The NMI supports the metrological infrastructure in that country by establishing an unbroken chain, from the top level of standards to an instrument used for measurement. Examples of National Metrology Institutes are NPL in the UK, NIST in the United States, PTB in Germany and many others. Establishing traceability is accomplished to a standard, indirectly related to certified reference materials. This may be done by national standards laboratories operated by the government or by private firms offering metrology services. Quality management systems call for an effective metrology system which includes formal, periodic, documented calibration of all measuring instruments. ISO 9000 and ISO 17025 standards require that these traceable actions are to a high level and set out how they can be quantified. To communicate the quality of a calibration the calibration value is often accompanied by a traceable uncertainty statement to a stated confidence level. This is evaluated through careful uncertainty analysis. Some times a DFS is required to operate machinery in a degraded state. Whenever this does happen, it must be in writing and authorized by a manager with the technical assistance of a calibration technician. Measuring devices and instruments are categorized according to the physical quantities they are designed to measure. These vary internationally, e.g. NIST 150-2G in the U.S. and NABL-141 in India.
Calibration
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An example of a device whose calibration is off: a weighing scale that reads ½ ounce without any load.
Calibration
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Indirect reading design showing a Bourdon tube from the front (left) and the rear (right).
Calibration
Calibration
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Gas pump with rotary flow indicator (yellow) and nozzle (red)
190.
Beam balance
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Weighing scales are devices to measure weight or calculate mass. Balances are widely used in commerce, as many products are sold and packaged by weight. Very accurate balances, called analytical balances are used in scientific fields such as chemistry. By the 1940s electronic devices were being attached to these designs to make readings more accurate. A scale measures weight by reporting the distance that a spring deflects under a load. Spring scales force, the tension force of constraint acting on an object, opposing the local force of gravity. They are usually calibrated so that measured force translates at earth's gravity. The object to be weighed can be set on a pivot and bearing platform. In a scale, the spring either stretches or compresses. By Hooke's law, every spring has a proportionality constant that relates how hard it is pulled to how far it stretches. Pinion mechanisms are often used to convert the linear spring motion to a dial reading. With proper setup, however, spring scales can be rated as legal for commerce. To remove the error, a commerce-legal spring scale must either have temperature-compensated springs or be used at a fairly constant temperature. To eliminate the effect of gravity variations, a commerce-legal scale must be calibrated where it is used. It is also common in high-capacity applications such as crane scales to use hydraulic force to weight.
Beam balance
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Digital kitchen scale, a strain gauge scale
Beam balance
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Scales used for trade purposes in the state of Florida, as this scale at the checkout in a cafeteria, are inspected for accuracy by the FDACS's Bureau of Weights and Measures.
Beam balance
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A two-pan balance
Beam balance
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Two 10- decagram masses
191.
Ernst Mach
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Ernst Waldfried Josef Wenzel Mach was an Austrian physicist and philosopher, noted for his contributions to physics such as study of shock waves. The ratio of one's speed to that of sound is named the Mach number in his honor. Ernst Waldfried Josef Wenzel Mach was born in Brno-Chrlice, Moravia. His father, who had graduated from Charles University in Prague, acted to the noble Brethon family in Zlín, eastern Moravia. His grandfather, an administrator of the estate Chirlitz, was also master builder of the streets there. His activities in that field later influenced the theoretical work of Ernst Mach. Some sources give Mach's birthplace as Turas/Tu the site of the Chirlitz registry-office. Peregrin Weiss baptized Ernst Mach in Turas/Tu řany. Despite his Catholic background, he later became his theory and life is compared with Buddhism. Up to the age of 14, Mach received his education from his parents. He then entered a Gymnasium in Kroměříž, where he studied for three years. In 1855 he became a student at the University of Vienna. There he for one semester medical physiology, receiving his doctorate in physics in 1860 and his Habilitation the following year. His early work focused in optics and acoustics. During that period, Mach continued his work in sensory perception.
Ernst Mach
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Ernst Mach (1838–1916)
Ernst Mach
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Ernst Mach’s photography of a bow shockwave around a supersonic bullet, in 1888.
Ernst Mach
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Bust of Mach in the Rathauspark (City Hall Park) in Vienna, Austria.
Ernst Mach
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Spinning chair devised by Mach to investigate the experience of motion
192.
Operationalization
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Operationalization is thus the process of defining a fuzzy concept so as to make it clearly distinguishable, measurable, understandable in terms of empirical observations. In a wider sense, it refers to the process of specifying the extension of a concept—describing what is and is not an instance of that concept. In medicine, the phenomenon of health might be operationalized like tobacco smoking. This is often called conducting a robustness check. If the results are unchanged, the results are said to be robust against certain alternative operationalizations of the checked variables. The concept of operationalization was first presented by the British physicist N. R. Campbell in his'Physics: The Elements'. This concept next spread to humanities and social sciences. It remains in use in physics. This comes from the philosophy of science book The Logic of Modern Physics, by Percy Williams Bridgman, whose methodological position is called operationalism. Bridgman's theory was criticized because we measure "length" in various ways, "length" logically isn't one concept but many, some concepts requiring knowledge of geometry. Each concept is to be defined by the measuring operations used. Another example is the radius of a sphere, obtaining different values depending on the way it is measured. Bridgman said the concept is defined on the measurement. Bridgman notes that in the theory of relativity we see how a concept like "duration" can split into multiple different concepts. However, Bridgman proposes that if we only stick to operationally defined concepts, this will never happen.
Operationalization
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An example of operationally defining "personal space".
193.
Percy W. Bridgman
–
Percy Williams Bridgman was an American physicist who won the 1946 Nobel Prize in Physics for his work on the physics of high pressures. Bridgman also wrote extensively on other aspects of the philosophy of science. Known as "Peter", he was born in Cambridge, Massachusetts, grew up in nearby Auburndale, Massachusetts. Bridgman's parents were both born in New England. Worked as a newspaper reporter assigned to state politics. Mary Ann Maria Williams, was described as "more conventional, sprightly, competitive". He attended both high school in Auburndale, where he excelled at competitions in the classroom, on the playground, while playing chess. Described as both proud, his home life consisted of family music, card games, domestic and garden chores. The family was deeply religious; attending a Congregational Church. He studied physics through to his Ph.D.. Until his retirement Bridgman taught at Harvard, becoming a full professor in 1919. In 1905, Bridgman began investigating the properties of matter under high pressure. A malfunction led him to modify his pressure apparatus; the result was a new device enabling him to create pressures eventually exceeding 100,000 kgf/cm2. This was a huge improvement over previous machinery, which could achieve pressures of only 3,000 kgf/cm2. He is also known in metals and properties of crystals.
Percy W. Bridgman
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Percy Williams Bridgman
194.
Newton's second law
–
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between the forces acting upon it, its motion in response to those forces. They can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to investigate the motion of many physical objects and systems. In this way, even a planet can be idealised around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of any particle structure. Newton's laws hold only to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed after Newton's death. In the given mass, acceleration, momentum, force are assumed to be externally defined quantities. Not the only interpretation of the way one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a constant, as, ∑ F = 0 ⇔ d v d t = 0.
Newton's second law
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Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's second law
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Isaac Newton (1643–1727), the physicist who formulated the laws
195.
Newton's third law
–
Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, its motion in response to those forces. They have been expressed in several different ways, over nearly three centuries, can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, first published in 1687. Newton used them to explain and investigate the motion of many physical objects and systems. In this way, even a planet can be idealised as a particle for analysis of its orbital motion around a star. In their original form, Newton's laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Euler's laws can, however, be taken as axioms describing the laws of motion for extended bodies, independently of any particle structure. Newton's laws hold only with respect to a certain set of frames of reference called Newtonian or inertial reference frames. Other authors do treat the first law as a corollary of the second. The explicit concept of an inertial frame of reference was not developed until long after Newton's death. In the given mass, force are assumed to be externally defined quantities. This is the most common, but not the only interpretation of the way one can consider the laws to be a definition of these quantities. The first law states that if the net force is zero, then the velocity of the object is constant. The first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F = 0 ⇔ d v d t = 0.
Newton's third law
–
Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's third law
–
Isaac Newton (1643–1727), the physicist who formulated the laws
196.
Binding energy
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Binding energy is the energy required to disassemble a whole system into separate parts. A bound system typically has a lower potential energy than the sum of its constituent parts; this is what keeps the system together. Often this means that energy is released upon the creation of a bound state. This definition corresponds to a positive binding energy. System mass is not conserved in this process because the system is "open" during the binding process. There are several types of each operating over a different distance and scale. The smaller the scale of a bound system, the higher its associated binding energy. In astrophysics, the gravitational binding energy of a celestial body is the energy required to expand the material to infinity. If a carbon-12 body had the mass and radius of the Sun, its gravitational binding energy would be about 14.24 keV per atom. At the molecular level, bond-dissociation energy are measures of the binding energy between the atoms in a bond. It is the energy required to disassemble a molecule into its constituent atoms. This energy appears as energy, such as that released in chemical explosions, biological processes. Bond energies and bond-dissociation energies are typically in the range of few eV per bond. For example, the bond-dissociation energy of a carbon-carbon bond is about 3.6 eV. At the atomic level, the atomic binding energy of the atom derives from electromagnetic interaction, mediated by photons.
Binding energy
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Nuclear physics
197.
Deuterium
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Deuterium is one of two stable isotopes of hydrogen. Deuterium has a natural abundance of about one atom in 7003642000000000000 ♠ 6420 of hydrogen. Thus deuterium accounts for approximately 0.0156% of all the naturally occurring hydrogen in the oceans, while the most common isotope accounts for more than 99.98%. The abundance of deuterium changes slightly to another. The isotope's name is formed from the Greek deuteros meaning "second", to denote the two particles composing the nucleus. Deuterium was named in 1931 by Harold Urey. Urey won the Nobel Prize in 1934. Soon after deuterium's discovery, others produced samples of "heavy water" in which the deuterium content had been highly concentrated. Deuterium is destroyed in the interiors of stars faster than it is produced. Natural processes are thought to produce only an insignificant amount of deuterium. This is the ratio found in the giant planets, such as Jupiter. However, other astronomical bodies are found to have different ratios of deuterium to hydrogen-1. This is thought to be as a result of isotope separation processes that occur from solar heating of ices in comets. Like the water-cycle in Earth's weather, such heating processes may enrich deuterium to protium. The analysis of deuterium/protium ratios in comets found results very similar to the mean ratio in Earth's oceans.
Deuterium
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Deuterium discharge tube
Deuterium
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Full table
Deuterium
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Ionized deuterium in a fusor reactor giving off its characteristic pinkish-red glow
Deuterium
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Harold Urey
198.
International Bureau of Weights and Measures
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The organisation is usually referred to by its French initialism, BIPM. These organizations are also commonly referred to by their French initialisms. The BIPM was created on 20 May 1875, following the signing of the Metre Convention, a treaty among 51 nations. Under the authority of the Metric Convention, the BIPM helps to ensure uniformity of SI weights and measures around the world. The BIPM carries out measurement-related research. It takes part in and organises international comparisons of national measurement standards and performs calibrations for member states. The BIPM has an important role in maintaining accurate worldwide time of day. It combines, analyses, averages the official atomic time standards of member nations around the world to create a single, official Coordinated Universal Time. The BIPM is also the keeper of the international prototype of the kilogram. Milton. Metrologia Institute for Reference Materials and Measurements International Organization for Standardization National Institute of Standards and Technology Official website
International Bureau of Weights and Measures
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Pavillon de Breteuil in Sèvres, France.
International Bureau of Weights and Measures
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Seal of the BIPM
199.
Proposed redefinition of SI base units
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The metric system was originally conceived as a system of measurement, derivable from nature. When the metric system was first introduced in 1799 technical problems necessitated the use of artifacts such as the prototype metre and kilogram. If the proposed redefinition is accepted, the metric system will, for the first time, be wholly derivable from nature. The proposal can be summarised as follows: There will still be the same seven base units. It is only necessary to edit their present definitions. The new definitions will improve the SI without changing the size of any units, thus ensuring continuity with present measurements. Further details are found in the chapter of the Ninth SI Units Brochure. SI is structured around seven base units that have another twenty units that are derived from these base units. Although the units themselves form a coherent system, the definitions do not. The proposal before the CIPM seeks to remedy this by using the fundamental quantities of nature as the basis for deriving the base units. This will mean, amongst other things, that the kilogram will cease to be used as the definitive replica of the kilogram. The metre are already defined in such a manner. The basic structure of SI was developed over a period of about 170 years. Since 1960 technological advances have made it possible to address various weaknesses on an artifact to define the kilogram. Kilogramme des Archives were defined in terms of artefacts that were a "best attempt" at fulfilling these principles.
Proposed redefinition of SI base units
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Mass drift over time of national prototypes K21–K40, plus two of the International Prototype Kilogram 's (IPK's) sister copies: K32 and K8(41). All mass changes are relative to the IPK.
Proposed redefinition of SI base units
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Current (2013) SI system: Dependence of base unit definitions on other base units (for example, the metre is defined in terms of the distance traveled by light in a specific fraction of a second)
Proposed redefinition of SI base units
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A watt balance which is being used to measure the Planck constant in terms of the international prototype kilogram.
Proposed redefinition of SI base units
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A near-perfect sphere of ultra-pure silicon - part of the Avogadro project, an International Avogadro Coordination project to determine the Avogadro number
200.
Mass in special relativity
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Mass in special relativity incorporates the general understandings from the concept of mass–energy equivalence. Roche states that about 60 % of modern authors just avoid relativistic mass. For a discussion of mass in general relativity, see mass in general relativity. For a general discussion including mass in Newtonian mechanics, see the article on mass. The mass is another name for the rest mass of single particles. The more general mass loosely corresponds to the "rest mass" of a "system". Under such circumstances the mass is equal to the relativistic mass, the total energy of the system divided by c2. The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in relative motion. Because of this, it is often employed for systems which consist of widely separated high-energy particles. It is often convenient in calculation that the invariant mass of a system is the total energy of the system in the COM frame. The term relativistic mass is also sometimes used. This is the sum quantity of energy in a body or system. As seen from the center of frame, the relativistic mass is also the invariant mass, as discussed above. For other frames, the relativistic mass is larger the faster the body moves.
Mass in special relativity
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Dependency between the rest mass and E, given in 4-momentum (p 0, p 1) coordinates; p 0 c = E
201.
Relativistic mass
–
Mass in special relativity incorporates the general understandings from the concept of mass–energy equivalence. Roche states that about 60 % of modern authors just avoid relativistic mass. For a discussion of mass in general relativity, see mass in general relativity. For a general discussion including mass in Newtonian mechanics, see the article on mass. The mass is another name for the rest mass of single particles. The more general mass loosely corresponds to the "rest mass" of a "system". Under such circumstances the mass is equal to the relativistic mass, the total energy of the system divided by c2. The concept of invariant mass does not require bound systems of particles, however. As such, it may also be applied to systems of unbound particles in relative motion. Because of this, it is often employed for systems which consist of widely separated high-energy particles. It is often convenient in calculation that the invariant mass of a system is the total energy of the system in the COM frame. The term relativistic mass is also sometimes used. This is the sum quantity of energy in a body or system. As seen from the center of frame, the relativistic mass is also the invariant mass, as discussed above. For other frames, the relativistic mass is larger the faster the body moves.
Relativistic mass
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Dependency between the rest mass and E, given in 4-momentum (p 0, p 1) coordinates; p 0 c = E
202.
Speed of light
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The speed of light in vacuum, commonly denoted c, is a universal physical constant important in many areas of physics. According to special relativity, c is the maximum speed at which all matter and hence information in the universe can travel. It is the speed at which all massless particles and changes of the associated fields travel in vacuum. Such waves travel at c regardless of the inertial reference frame of the observer. In the theory of relativity, c interrelates space and time, also appears in the famous equation of mass–energy equivalence E = mc2. The ratio between the v at which light travels in a material is called the refractive index n of the material. In communicating with distant space probes, it can take minutes to hours for a message to get to the spacecraft, or versa. The light seen from stars left them many years ago, allowing the study of the history of the universe by looking at distant objects. The finite speed of light also limits the maximum speed of computers, since information must be sent to chip. The speed of light can be used with time of flight measurements to measure large distances to high precision. Ole Rømer first demonstrated in 1676 that light travels at a finite speed by studying the apparent motion of Jupiter's moon Io. In 1865, James Clerk Maxwell proposed that light was an electromagnetic wave, therefore travelled at the speed c appearing in his theory of electromagnetism. In 1983, the metre was redefined in the International System of Units as the distance travelled in ♠ 299792458 of a second. As a result, the numerical value of c in metres per second is now fixed exactly by the definition of the metre. The speed of light in vacuum is usually denoted by a lowercase c, for "constant" or the Latin celeritas.
Speed of light
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One of the last and most accurate time of flight measurements, Michelson, Pease and Pearson's 1930-35 experiment used a rotating mirror and a one-mile (1.6 km) long vacuum chamber which the light beam traversed 10 times. It achieved accuracy of ±11 km/s
Speed of light
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Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth.
Speed of light
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Diagram of the Fizeau apparatus
Speed of light
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Rømer's observations of the occultations of Io from Earth
203.
Lorentz factor
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The Lorentz factor or Lorentz term is the factor by which time, length, relativistic mass change for an object while that object is moving. It arises in derivations of the Lorentz transformations. The name originates from its earlier appearance in Lorentzian electrodynamics – named after the Dutch physicist Hendrik Lorentz. Due to its ubiquity, it is generally denoted with the γ. Sometimes the factor is written as Γ rather than γ. τ is the proper time for an observer, t is coordinate time c is the speed of light in a vacuum. This is the most frequently used form in practice, though not the only one. To complement the definition, some authors define the reciprocal: α 2 / c 2, see velocity addition formula. The middle column shows the corresponding Lorentz factor, the final is the reciprocal. Values in bold are exact. There are other ways to write the factor. Related variables such as momentum and rapidity may also be convenient. Thus the parameter forms a one-parameter group, a foundation for physical models. The γ ≈ 1 + 1/2 β2 may be used to calculate relativistic effects at low speeds. It holds to within 0.1 % error for v < 0.22 c.
Lorentz factor
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Lorentz factor γ as a function of velocity. Its initial value is 1 (when v = 0); and as velocity approaches the speed of light (v → c) γ increases without bound (γ → ∞).
204.
Relativistic energy-momentum equation
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Unlike either of those equations, the energy-momentum equation relates the total energy to the rest m0. All three equations hold true simultaneously. Special cases of the relation include: If the body is a massless particle, then reduces to E = pc. For photons, this is the relation, discovered in 19th century classical electromagnetism, between radiant momentum and energy. A more general form of relation holds for general relativity. Although we still have, in flat spacetime; E ′ 2 − 2 = 2. P, E ′, p ′ are all related by a Lorentz transformation. The relation allows one to sidestep Lorentz transformations when determining only the magnitudes of the momenta by equating the relations in the different frames. Again in flat spacetime, this translates to; E 2 2 = E ′ 2 − 2 = 2. In relativistic quantum theory, it is applicable to all particles and fields. This is completely general for all is easy to extend to multi-particle systems. This approach is not general as particles are not considered. No energy-momentum relation could be derived, not correct. In Minkowski space, momentum are two components of a Minkowski four-vector, namely the four-momentum; P =. Then: P α g β P β = 2.
Relativistic energy-momentum equation
205.
Rest energy
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System momentum is subtracted from this, so that the invariant mass remains unchanged. Systems whose four-momentum is a null vector are referred to as massless. These do not appear to exist. Any time-like four-momentum possesses a frame where the momentum is zero, a center of momentum frame. In this case, mass is positive and is referred to as the rest mass. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. The same is true for massless particles in such system, which add invariant mass and also rest mass according to their energy. For an massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it. In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total energy divided by c2. Note that for reasons above, such a frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame exists. For example, invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, mass is in general not an additive quantity.
Rest energy
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Possible 4-momenta of particles. One has zero invariant mass, the other is massive
206.
Pedagogy
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Pedagogy is the discipline that deals with the theory and practice of education; it thus concerns the study of how best to teach. Spanning a broad range of practice, its aims range from furthering liberal education to the narrower specifics of vocational education. Instructive strategies are governed by environment, well as learning goals set by the student and teacher. One example would be the Socratic schools of thought. The teaching of adults, as a specific group, is referred to as andragogy. Johann Friedrich Herbart is the founding father of the conceptualization of pedagogy, or, the theory of education. Herbart's educational philosophy and pedagogy highlighted the correlation between personal development and the resulting benefits to society. In other words, Herbart proposed that humans become fulfilled once they establish themselves as productive citizens. Herbartianism refers to the movement underpinned by Herbart's theoretical perspectives. Referring to the teaching process, Herbart suggested 5 steps as crucial components. Specifically, these 5 steps include: application. Herbart suggests that pedagogy relates to having assumptions as an educator and a specific set of abilities with a deliberate end goal in mind. The word is a derivative of the Greek παιδαγωγία, from παιδαγωγός, itself a synthesis of ἄγω, "I lead", παῖς "child": hence, "to lead a child." It is pronounced variously, as /ˈpɛdəɡɒdʒi/, /ˈpɛdəɡoʊdʒi/, or /ˈpɛdəɡɒɡi/. Negative connotations of pedantry have sometimes been intended, or taken, at least from the time of Samuel Pepys in the 1650s.
Pedagogy
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Douris Man with wax tablet
Pedagogy
207.
Atomic nuclei
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After the discovery of the neutron in 1932, models for a nucleus composed of neutrons were quickly developed by Dmitri Ivanenko and Werner Heisenberg. Almost all of the mass of an atom is located with a very small contribution from the electron cloud. Neutrons are bound together to form a nucleus by the nuclear force. The diameter of the nucleus is in the range of 6985175000000000000♠1.75 fm for hydrogen to about 6986150000000000000♠15 fm for the heaviest atoms, such as uranium. These dimensions are much smaller by a factor of about 23,000 to about 145,000. The nucleus was discovered as a result of Ernest Rutherford's efforts to test Thomson's "plum pudding model" of the atom. The electron had already been discovered earlier by J.J. Thomson himself. Knowing that atoms are electrically neutral, Thomson postulated that there must be a positive charge well. In his plum model, Thomson suggested that an atom consisted of negative electrons randomly scattered within a sphere of positive charge. To his surprise, many of the particles were deflected at very large angles. This justified the idea of a nuclear atom with a dense center of positive mass. The nucleus is from the Latin word nucleus, a diminutive of nux, meaning the kernel inside a watery type of fruit. In 1844, Michael Faraday used the term to refer to the "central point of an atom". The atomic meaning was proposed by Ernest Rutherford in 1912.
Atomic nuclei
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Nuclear physics
208.
Nuclide
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The nuclide was proposed by Truman P. Kohman in 1947. Kohman originally suggested nuclide as referring to a "species of nucleus" defined by containing a certain number of protons. The word thus was originally intended to focus on the nucleus. Nuclide refers to a nucleus rather than to an atom. Identical nuclei belong for example each nucleus of the carbon-13 nuclide is composed of 6 protons and 7 neutrons. The nuclide concept emphasizes nuclear properties over chemical properties, while the isotope concept emphasizes chemical over nuclear. Its effect on chemical properties is negligible for most elements. I.e. of the same chemical element but different neutron numbers, are called isotopes of the element. The term "nuclide" is the correct one in general. See Isotope #Notation for an explanation of the notation used for different isotope types. Nuclear isomers are different states of excitation. An example is the two states of the single isotope 99 43Tc shown among the decay schemes. Each of these two states qualifies as a different nuclide, illustrating one way that nuclides may differ from isotopes. The most non-ground state nuclear isomer is the nuclide tantalum-180m, which has a half-life in excess of 1,000 trillion years. This nuclide has never been observed to decay to the ground state.
Nuclide
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Nuclear physics
209.
Nucleon
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In chemistry and physics, a nucleon is one of the particles that make up the atomic nucleus. Each atom in turn consists of a cluster of nucleons surrounded by one or more electrons. There are two known kinds of nucleon: the proton. The mass number of a given atomic isotope is identical to its number of nucleons. Thus the term number may be used in place of the more common terms mass number or atomic mass number. Until the 1960s, nucleons were thought to be elementary particles, each of which would not then have been made up of smaller parts. Now they are known to be composite particles, made of three quarks bound together by the strong interaction. The interaction between two or more nucleons is called nuclear force, also ultimately caused by the strong interaction. Nucleons sit at the boundary where nuclear physics overlap. Particle physics, particularly quantum chromodynamics, provides the fundamental equations that explain the properties of the strong interaction. These equations explain quantitatively how quarks can bind together into neutrons. However, when multiple nucleons are assembled into an atomic nucleus, these fundamental equations become too difficult to solve directly. Instead, nuclides are studied within nuclear physics, which studies their interactions by approximations and models, such as the nuclear shell model. These models can successfully explain nuclide properties, for example, whether or not a certain nuclide undergoes radioactive decay. The neutron are both baryons and both fermions.
Nucleon
210.
Thermal energy
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In thermodynamics, thermal energy refers to the internal energy present in a system due to its temperature. Instead, the thermodynamic concept is heat, defined as a transfer of energy. Work therefore depend on the path of transfer and are not state functions, whereas internal energy is a state function. Heat is energy transferred spontaneously to a colder system or body. Heat is energy in transfer, not a property of the system; it is not contained within the boundary of the system. On the other hand, internal energy exists on both sides of a boundary. The internal energy of an ideal gas can in this sense be regarded as "thermal energy". In this case, however, internal energy are identical. Systems that are more complex than ideal gases can undergo phase transitions. Phase transitions can change the internal energy of the system without changing its temperature. Therefore, the thermal energy cannot be defined solely by the temperature. For these reasons, the concept of the thermal energy of a system is not used in thermodynamics. In an 1847 lecture entitled On Matter, Heat, James Prescott Joule characterized various terms that are closely related to thermal energy and heat. Heat transfer Ocean thermal energy conversion Thermal science Example of incorrect use of heat and thermal energy
Thermal energy
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Thermal radiation in visible light can be seen on this hot metalwork. Thermal energy would ideally be the amount of heat required to warm the metal to its temperature, but this quantity is not well-defined, as there are many ways to obtain a given body at a given temperature, and each of them may require a different amount of total heat input. Thermal energy, unlike internal energy, is therefore not a state function.
211.
Latent heat
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Latent heat is energy released or absorbed, by a body or a thermodynamic system, during a constant-temperature process. An example is latent heat at a specified temperature and pressure. The term was introduced by Scottish chemist Joseph Black. It is derived from the Latin latere. Black used the term in the context of calorimetry where a transfer caused a volume change while the thermodynamic system's temperature was constant. In contrast to heat, sensible heat involves an energy transfer that results in a temperature change of the system. The terms ″ ″ latent heat ″ are specific forms of energy; they are two properties of a material or in a thermodynamic system. ″ Sensible heat ″ is a body's internal energy that may be ″ felt. ″ Latent heat ″ does not affect the temperature. Both latent heats are observed in many processes of transport of energy in nature. The original usage of the term, as introduced by Black, was applied to systems that were intentionally held at constant temperature. Several other related latent heats. These latent heats are defined independently of the conceptual framework of thermodynamics. Two common forms of heat are latent heat of fusion and latent heat of vaporization. These names describe the direction of flow when changing from one phase to the next: from solid to liquid, liquid to gas.
Latent heat
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State
212.
Conservation of energy
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In physics, the law of conservation of energy states that the total energy of an isolated system remains constant—it is said to be conserved over time. Energy destroyed; rather, it transforms from one form to another. For instance, energy can be converted to kinetic energy in the explosion of a stick of dynamite. A consequence of the law of conservation of energy is that a perpetual machine of the first kind can not exist. That is to say, no system without an external supply can deliver an unlimited amount of energy to its surroundings. Ancient philosophers as back as Thales of Miletus c. 550 BCE had inklings of the conservation of some underlying substance of which everything is made. However, there is no particular reason to identify this with what we know today as "mass-energy". Empedocles wrote that in his universal system, composed of four roots, "nothing perishes"; instead, these elements suffer continual rearrangement. In 1605, Simon Stevinus was able to solve a number of problems in statics based on the principle that perpetual motion was impossible. In 1669, Christian Huygens published his laws of collision. However, the difference between inelastic collision was not understood at the time. This led as to which of these conserved quantities was the more fundamental. Huygens' study of the dynamics of motion was based on a single principle: that the center of gravity of heavy objects can not lift itself. It was Leibniz during 1676–1689 who first attempted a mathematical formulation of the kind of energy, connected with motion. He called living force of the system.
Conservation of energy
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Gottfried Leibniz
Conservation of energy
–
Gaspard-Gustave Coriolis
Conservation of energy
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James Prescott Joule
213.
Mass in general relativity
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The concept of mass in general relativity is more complex than the concept of mass in special relativity. In fact, general relativity offers several different definitions that are applicable under different circumstances. Under some circumstances, the mass of a system in general relativity may not even be defined. How, then, does one define a concept as a system's total mass –, easily defined in classical mechanics? A non-technical definition of a stationary spacetime is a spacetime where none of the metric coefficients g ν are functions of time. The Schwarzschild metric of the Kerr metric of a rotating black hole are common examples of stationary spacetimes. By definition, a stationary spacetime exhibits time symmetry. This is technically called a time-like vector. Because the system has a time symmetry, Noether's theorem guarantees that it has a conserved energy. In general relativity, this mass is called the Komar mass of the system. Komar mass can only be defined for stationary systems. Komar mass can also be defined by a flux integral. This is similar to the way that Gauss's law defines the charge enclosed as the normal electric force multiplied by the area. See the main article for more detail. Of the two definitions, the description of Komar mass in terms of a time symmetry provides the deepest insight.
Mass in general relativity
–
General relativity
214.
Gravitational mass
–
In physics, mass is a property of a physical body. It is the measure of an object's resistance to acceleration when a force is applied. It also determines the strength of its gravitational attraction to other bodies. In the theory of relativity a related concept is the mass -- content of a system. The SI unit of mass is the kilogram. It would still have the same mass. This is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized in an object. However, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, all forms of energy resist acceleration by a force and have gravitational attraction. In addition, "matter" thus can not be precisely measured. There are distinct phenomena which can be used to measure mass. Gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the gravitational force exerted on an object in a gravitational field. Mass–energy measures the total amount of energy contained within a body, using E = mc2.
Gravitational mass
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Depiction of early balance scales in the Papyrus of Hunefer (dated to the 19th dynasty, ca. 1285 BC). The scene shows Anubis weighing the heart of Hunefer.
Gravitational mass
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The kilogram is one of the seven SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).
Gravitational mass
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Galileo Galilei (1636)
Gravitational mass
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Distance traveled by a freely falling ball is proportional to the square of the elapsed time
215.
Inertial mass
–
In physics, mass is a property of a physical body. It is the measure of an object's resistance to acceleration when a force is applied. It also determines the strength of its gravitational attraction to other bodies. In the theory of relativity a related concept is the mass -- content of a system. The SI unit of mass is the kilogram. It would still have the same mass. This is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized in an object. However, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, all forms of energy resist acceleration by a force and have gravitational attraction. In addition, "matter" thus can not be precisely measured. There are distinct phenomena which can be used to measure mass. Gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the gravitational force exerted on an object in a gravitational field. Mass–energy measures the total amount of energy contained within a body, using E = mc2.
Inertial mass
–
Depiction of early balance scales in the Papyrus of Hunefer (dated to the 19th dynasty, ca. 1285 BC). The scene shows Anubis weighing the heart of Hunefer.
Inertial mass
–
The kilogram is one of the seven SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).
Inertial mass
–
Galileo Galilei (1636)
Inertial mass
–
Distance traveled by a freely falling ball is proportional to the square of the elapsed time
216.
Invariant mass
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System momentum is subtracted from this, so that the invariant mass remains unchanged. Systems whose four-momentum is a null vector are referred to as massless. These do not appear to exist. Any time-like four-momentum possesses a frame where the momentum is zero, a center of momentum frame. In this case, mass is positive and is referred to as the rest mass. This is also equal to the total energy of the system divided by c2. See mass–energy equivalence for a discussion of definitions of mass. The same is true for massless particles in such system, which add invariant mass and also rest mass according to their energy. For an massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity. Thus, an observer can always be placed to move along with it. In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total energy divided by c2. Note that for reasons above, such a frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame exists. For example, invariant mass are zero for individual photons even though they may add mass to the invariant mass of systems. For this reason, mass is in general not an additive quantity.
Invariant mass
–
Possible 4-momenta of particles. One has zero invariant mass, the other is massive
217.
Nonlinear system
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In physical sciences, a nonlinear system is a system in which the output is not directly proportional to the input. Nonlinear problems are to many other scientists because most systems are inherently nonlinear in nature. Nonlinear systems may appear counterintuitive, contrasting with the much simpler linear systems. It does not matter if nonlinear known functions appear in the equations. As nonlinear equations are difficult to solve, nonlinear systems are commonly approximated by linear equations. It follows that some aspects of the behavior of a system appear commonly to be counterintuitive, even chaotic. Although chaotic behavior may resemble random behavior, it is not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout. This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology. Some authors use the science for the study of nonlinear systems. This is disputed by others: Using a term like science is like referring as the study of non-elephant animals. Additivity implies homogeneity for any rational α, and, for continuous functions, for any real α. For a complex α, homogeneity does not follow from additivity. For example, an antilinear map is additive but not homogeneous. The equation is called homogeneous if C = 0.
Nonlinear system
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Linearizations of a pendulum
218.
Wave function
–
A wave function in quantum mechanics is a description of the quantum state of a system. The probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a function are the Greek letters ψ or Ψ. The function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the function can be derived from the quantum state. The wave function for such particles includes spin as an intrinsic, discrete degree of freedom. Discrete variables can also be included, such as isospin. These values are often displayed in a matrix. The Schrödinger equation determines how wave functions evolve over time. This gives rise to wave -- particle duality. Since the function is complex valued, only its relative phase and relative magnitude can be measured. The equations represent wave -- duality for both massless and massive particles. In the 1930s, quantum mechanics was developed using calculus and linear algebra. Those who used the techniques of calculus included Louis de Broglie, others, developing "wave mechanics". Those who applied the methods of linear algebra included Werner Heisenberg, others, developing "matrix mechanics".
Wave function
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The electron probability density for the first few hydrogen atom electron orbitals shown as cross-sections. These orbitals form an orthonormal basis for the wave function of the electron. Different orbitals are depicted with different scale.
219.
Covariance and contravariance of vectors
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In multilinear algebra and tensor analysis, covariance and contravariance describe how the quantitative description of certain geometric or physical entities changes with a change of basis. In physics, a basis is sometimes thought of as a set of reference axes. A change of scale on the reference axes corresponds to a change of units in the problem. In changing scale from meters to centimeters, the components of a measured vector will multiply by 100. Vectors exhibit this behavior of changing scale inversely to changes in scale to the reference axes: they are contravariant. As a result, vectors often have units of distance or distance times some other unit. In contrast, dual vectors typically have units the inverse of distance or the inverse of distance times some other unit. An example of a dual vector is the gradient, which has − 1. The components of dual vectors change in the same way as changes to scale of the reference axes: they are covariant. That is, the matrix that transforms the vector of components must be the inverse of the matrix that transforms the basis vectors. The components of vectors are said to be contravariant. In Einstein notation, contravariant components are denoted with upper indices as in v = v i e i. For a dual vector to be basis-independent, the components of the dual vector must co-vary with a change of basis to remain representing the same covector. That is, the components must be transformed by the same matrix as the change of basis matrix. The components of dual vectors are said to be covariant.
Covariance and contravariance of vectors
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tangent basis vectors (yellow, left: e 1, e 2, e 3) to the coordinate curves (black),
220.
Dirac equation
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In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. Including electromagnetic interactions, it describes all spin-1 / 2 massive particles such as electrons and quarks for which parity is a symmetry. It was validated by accounting for the fine details of the spectrum in a completely rigorous way. The equation also implied the existence of a new form of antimatter, previously unsuspected and unobserved and, experimentally confirmed several years later. Moreover, in the limit of zero mass, the Dirac equation reduces to the Weyl equation. This accomplishment has been described as fully before him. In the context of quantum theory, the Dirac equation is reinterpreted to describe quantum fields corresponding to spin-1 / 2 particles. The p1, p2, p3 are the components of the momentum, understood to be the operator in the Schrödinger equation. Also, ħ is the Planck constant divided by 2π. These physical constants reflect special relativity and quantum mechanics, respectively. His rather modest hope was that the corrections introduced this way might have a bearing on the problem of atomic spectra. The four-component wave function ψ. There are four components in ψ because the evaluation of it at any given point in space is a bispinor. It is interpreted as a superposition of a spin-up electron, a spin-down electron, a spin-down positron. The form of the wave function have a deep mathematical significance.
Dirac equation
221.
Natural units
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In physics, natural units are physical units of measurement based only on universal physical constants. For example, the elementary charge e is a natural unit of electric charge, the speed of light c is a natural unit of speed. In this case, the reinsertion of the correct powers of e, c, etc can be uniquely determined. Natural units are "natural" because the origin of their definition comes only from properties of nature and not from any human construct. Planck units are often, without qualification, called "natural units", although they constitute only one of several systems of natural units, albeit the best known such system. Virtually every system of natural units normalizes Boltzmann's constant kB to 1, which can be thought as simply a way of defining the temperature. Both possibilities are incorporated into different natural unit systems. Natural units are most commonly used by setting the units to one. For example, natural unit systems include the c = 1 in the unit-system definition, where c is the speed of light. If a v is half the speed of light, then as c = 1, hence v = 1/2. The equation c = 1 can be plugged in anywhere else. For example, Einstein's = mc2 can be rewritten in Planck units as E = m. This equation means "The energy of a particle, measured in Planck units of energy, equals the mass of the particle, measured in Planck units of mass." E2 = p2 + m2, appears simpler. Physical interpretation: Natural unit systems automatically subsume dimensional analysis.
Natural units
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Base units
222.
Higgs mechanism
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In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a quantum field that permeates all space, to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. The Higgs mechanism was incorporated into modern particle physics by Steven Weinberg and Abdus Salam, is an essential part of the standard model. At temperatures high enough that symmetry is unbroken, all elementary particles are massless. At a critical temperature, the Higgs field becomes tachyonic; the symmetry is spontaneously broken by condensation, the W and Z bosons acquire masses. In the standard model, the Higgs field is an SU doublet, a scalar under Lorentz transformations. Its U charge is 1. The Higgs field, through the interactions specified by its potential, induces spontaneous breaking out of the four generators of the group U. This is often written as SU × U, because the diagonal phase factor also acts on other fields in particular quarks. Three out of its four components would ordinarily amount to Goldstone bosons, if they were not coupled to gauge fields. The gauge group of the electroweak part of the standard model is SU × U. Rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor.
Higgs mechanism
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Large Hadron Collider tunnel at CERN
Higgs mechanism
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Philip W. Anderson, the first to propose the mechanism in 1962.
Higgs mechanism
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Five of the six 2010 APS Sakurai Prize Winners – (L to R) Tom Kibble, Gerald Guralnik, Carl Richard Hagen, François Englert, and Robert Brout
Higgs mechanism
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Number six: Peter Higgs 2009
223.
Higgs boson
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The Higgs boson is an elementary particle in the Standard Model of particle physics. It is the excitation of the Higgs field, a fundamental field of crucial importance to particle physics theory first suspected to exist in the 1960s. Unlike known fields such as the electromagnetic field, it has a non-zero constant value in vacuum. The existence of the Higgs field would also resolve several long-standing puzzles, such as the reason for the weak force's extremely short range. Although it is hypothesised that the Higgs field permeates the entire Universe, evidence for its existence has been very difficult to obtain. These are extremely difficult to produce and detect. Since then, the particle has been shown to interact, decay in many of the ways predicted by the Standard Model. It was also tentatively confirmed to have two fundamental attributes of a Higgs boson. This appears to be the elementary scalar particle discovered in nature. The Higgs boson is named after one of six physicists who, in 1964, proposed the mechanism that suggested the existence of such a particle. On December 2013, two of them, Peter Higgs and François Englert, were awarded the Nobel Prize in Physics for their work and prediction. Although Higgs's name has come to be associated with this theory, several researchers between about 1972 independently developed different parts of it. In the Standard Model, the Higgs particle is a boson with no spin, colour charge. It is also decaying into other particles almost immediately. It is a quantum excitation of the four components of the Higgs field.
Higgs boson
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Large Hadron Collider tunnel at CERN
Higgs boson
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Candidate Higgs boson events from collisions between protons in the LHC. The top event in the CMS experiment shows a decay into two photons (dashed yellow lines and green towers). The lower event in the ATLAS experiment shows a decay into 4 muons (red tracks).
Higgs boson
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The six authors of the 1964 PRL papers, who received the 2010 J. J. Sakurai Prize for their work. From left to right: Kibble, Guralnik, Hagen, Englert, Brout. Right: Higgs.
Higgs boson
224.
Electroweak symmetry breaking
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In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. The Higgs field resolves this conundrum. The simplest description of the mechanism adds a field that permeates all space, to the Standard Model. Below some extremely high temperature, the field causes spontaneous symmetry breaking during interactions. The breaking of symmetry triggers the Higgs mechanism, causing the bosons it interacts with to have mass. The Higgs mechanism is an essential part of the standard model. At temperatures high enough that electroweak symmetry is unbroken, all elementary particles are massless. At a critical temperature, the Higgs field becomes tachyonic; the W and Z bosons acquire masses. In the standard model, the Higgs field is an SU doublet, a scalar under Lorentz transformations. Its U charge is 1. The Higgs field, through the interactions specified by its potential, induces spontaneous breaking out of the four generators of the gauge group U. This is often written as SU × U, because the diagonal factor also acts on other fields in particular quarks. Three out of its four components would ordinarily amount to Goldstone bosons, if they were not coupled to gauge fields. The gauge group of the electroweak part of the standard model is SU × U. Rotating the coordinates so that the second basis vector points in the direction of the Higgs boson makes the vacuum expectation value of H the spinor.
Electroweak symmetry breaking
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Large Hadron Collider tunnel at CERN
Electroweak symmetry breaking
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Philip W. Anderson, the first to propose the mechanism in 1962.
Electroweak symmetry breaking
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Five of the six 2010 APS Sakurai Prize Winners – (L to R) Tom Kibble, Gerald Guralnik, Carl Richard Hagen, François Englert, and Robert Brout
Electroweak symmetry breaking
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Number six: Peter Higgs 2009
225.
Imaginary number
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The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, its square is −25. Zero is considered to be both real and imaginary. The concept had appeared in print earlier, for instance in work by Gerolamo Cardano. At the time, such numbers were poorly regarded by some as useless, much as zero and the negative numbers once were. The use of imaginary numbers was not widely accepted until the work of Leonhard Euler and Carl Friedrich Gauss. The geometric significance of complex numbers as points in a plane was first described by Caspar Wessel. This idea first surfaced beginning in 1848. Geometrically, imaginary numbers are found on the vertical axis of the complex number plane, allowing them to be presented perpendicular to the real axis. This vertical axis is denoted iℝ, ℑ. In this representation, multiplication by –1 corresponds to a rotation of 180 degrees about the origin. Note that a 90-degree rotation in the "negative" direction also satisfies this interpretation. This reflects the fact that −i also solves the equation x2 = −1. Care must be used when working with imaginary numbers expressed as the principal values of the square roots of negative numbers. For example: = 36 = ≠ − 4 − = = 6 i 2 = − 6.
Imaginary number
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An illustration of the complex plane. The imaginary numbers are on the vertical coordinate axis.
226.
Particle
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A particle is a minute fragment or quantity of matter. In the physical sciences, a particle is a small localized object to which can be ascribed several chemical properties such as volume or mass. Particles can also be used to create scientific models such as humans moving in a crowd or celestial bodies in motion. The term is refined as needed by various scientific fields. Something, composed of particles may be referred as being particulate. The concept of particles is particularly useful when modelling nature, as the full treatment of many phenomena can be complex. It can be used to make simplifying assumptions concerning the processes involved. Francis Sears and Mark Zemansky, in University Physics, give the example of calculating the landing speed of a baseball thrown in the air. The treatment of large numbers of particles is the realm of statistical physics. The term "particle" is usually applied differently to three classes of sizes. The term macroscopic particle, usually refers to particles much larger than molecules. These are usually abstracted as point-like particles, even though they have shapes, structures, etc.. Another type, microscopic particles usually refers to particles of sizes ranging from atoms to molecules, such as carbon dioxide, nanoparticles, colloidal particles. These particles are studied in chemistry, well as atomic and molecular physics. The smallest of particles are the subatomic particles, which refer to particles smaller than atoms.
Particle
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Arc welders need to protect themselves from welding sparks, which are heated metal particles that fly off the welding surface. Different particles are formed at different temperatures.
Particle
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Galaxies are so large that stars can be considered particles relative to them
227.
Faster-than-light
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Faster-than-light communication and travel refer to the propagation of information or matter faster than the speed of light. Examples of apparent FTL proposals are the traversable wormhole, although their physical plausibility is uncertain. This is not quite the same as traveling faster than light, since: Some processes can not carry information. Thus neither qualifies as FTL as described here. For an Earthbound observer, objects in the sky complete one revolution around the Earth in 1 day. Proxima Centauri, the nearest star outside the solar system, is about 4 light-years away. Comets may have orbits which take them out to more than 1000 AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, therefore non-inertial, frame. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does any information travel faster than light. Thus this change can not be used to transmit information from the source. No matter can be FTL-transmitted or propagated from source to receiver/observer by an electromagnetic field. The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. Imagine two fast-moving particles approaching each other from opposite sides of a accelerator of the collider type.
Faster-than-light
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History of the universe - gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang (17 March 2014).
228.
Causality
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In general, a process has many causes, which are said to be causal factors for it, all lie in its past. An effect can in turn be a cause of many other effects. The concept is like those of agency and efficacy. For this reason, a leap of intuition may be needed to grasp it. Accordingly, causality is built into the conceptual structure of ordinary language. In this case, failure to recognize that different kinds of "cause" are being considered can lead to futile debate. Of Aristotle's four explanatory modes, the one nearest to the concerns of the present article is the "efficient" one. The topic remains a staple in contemporary philosophy. While studying of meaning of causality semantics traditionally appeal to the egg dilemma, i.e. "which came first, the chicken or the egg?". Then it allocates its constituent elements: itself, that joins both of them. The nature of cause and effect is a concern of the subject known as metaphysics. A metaphysical question about effect is what kind of entity can be a cause, what kind of entity can be an effect. One viewpoint on this question is that cause and effect are of one and the same kind of entity, with causality an asymmetric relation between them. An example is ` his tripping over the step was his breaking the effect'. Another view is that effects are ` states of affairs', with the exact natures of those entities being less restrictively defined than in philosophy.
Causality
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The Illustrated Sutra of Cause and Effect. 8th century, Japan
Causality
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Key concepts
Causality
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Time Portal
229.
Phase transition
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The term phase transition is most commonly used to describe transitions between solid, liquid and gaseous states of matter, and, in rare cases, plasma. A phase of the states of matter have physical properties. For example, a liquid may become gas upon heating to the boiling point, resulting in an abrupt change in volume. The measurement of the external conditions at which the transformation occurs is termed the phase transition. Phase transitions are common in nature and used today in many technologies. The same process, but beginning with a solid instead of a liquid is called a eutectoid transformation. A peritectic transformation, in which a two component single phase solid transforms into a liquid phase. A spinodal decomposition, in which a single phase is cooled and separates into two different compositions of that same phase. Transition to a mesophase between solid and liquid, such as one of the "liquid crystal" phases. The transition between the ferromagnetic and paramagnetic phases of magnetic materials at the Curie point. The transition between differently ordered, commensurate or incommensurate, magnetic structures, such as in cerium antimonide. The martensitic transformation which occurs as one of the many phase transformations in carbon steel and stands as a model for displacive phase transformations. Changes in the crystallographic structure such as between ferrite and austenite of iron. Order-disorder transitions such as in alpha-titanium aluminides. The dependence of the adsorption geometry on coverage and temperature, such as for hydrogen on iron.
Phase transition
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A small piece of rapidly melting solid argon simultaneously shows the transitions from solid to liquid and liquid to gas.
Phase transition
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This diagram shows the nomenclature for the different phase transitions.
230.
Superluminal
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Faster-than-light communication and travel refer to the propagation of information or matter faster than the speed of light. Examples of apparent FTL proposals are the traversable wormhole, although their physical plausibility is uncertain. This is not quite the same as traveling faster than light, since: Some processes can not carry information. Thus neither qualifies as FTL as described here. For an Earthbound observer, objects in the sky complete one revolution around the Earth in 1 day. Proxima Centauri, the nearest star outside the solar system, is about 4 light-years away. Comets may have orbits which take them out to more than 1000 AU. The circumference of a circle with a radius of 1000 AU is greater than one light day. In other words, a comet at such a distance is superluminal in a geostatic, therefore non-inertial, frame. Similarly, a shadow projected onto a distant object can be made to move across the object faster than c. In neither case does any information travel faster than light. Thus this change can not be used to transmit information from the source. No matter can be FTL-transmitted or propagated from source to receiver/observer by an electromagnetic field. The rate at which two objects in motion in a single frame of reference get closer together is called the mutual or closing speed. Imagine two fast-moving particles approaching each other from opposite sides of a accelerator of the collider type.
Superluminal
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History of the universe - gravitational waves are hypothesized to arise from cosmic inflation, a faster-than-light expansion just after the Big Bang (17 March 2014).
231.
Ferromagnetism
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Not to be confused with Ferrimagnetism; for an overview see Magnetism. Ferromagnetism is the basic mechanism by which certain materials form permanent magnets, or are attracted to magnets. In physics, several different types of magnetism are distinguished. An everyday example of ferromagnetism is a refrigerator magnet used to hold notes on a refrigerator door. The attraction between a magnet and ferromagnetic material is "the quality of magnetism first apparent to the ancient world, to us today". Permanent magnets are either ferromagnetic or ferrimagnetic, as are the materials that are noticeably attracted to them. Only a few substances are ferromagnetic. Historically, the term ferromagnetism was used for any material that could exhibit spontaneous magnetization: a net magnetic moment in the absence of an external magnetic field. This general definition is still in common use. In particular, a material is "ferromagnetic" in this narrower sense only if all of its magnetic ions add a positive contribution to the net magnetization. If some of the magnetic ions subtract from the net magnetization, then the material is "ferrimagnetic". These alignment effects only occur at temperatures below a certain critical temperature, called the Curie temperature or the Néel temperature. Among the first investigations of ferromagnetism are the pioneering works of Aleksandr Stoletov on measurement of the magnetic permeability of ferromagnetics, known as the Stoletov curve. The table on the right lists a selection of ferromagnetic and ferrimagnetic compounds, along with the temperature above which they cease to exhibit spontaneous magnetization. Ferromagnetism is a property not just of the chemical make-up of a material, but of its crystalline structure and microstructure.
Ferromagnetism
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A magnet made of alnico, an iron alloy, with its keeper. Ferromagnetism is the theory which explains how materials become magnets.
232.
Condensed matter physics
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Condensed matter physics is a branch of physics that deals with the physical properties of condensed phases of matter, where particles adhere to each other. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics, electromagnetism and statistical mechanics. The field overlaps with chemistry, materials science, nanotechnology, relates closely to atomic physics and biophysics. Theoretical condensed matter physics shares important concepts and techniques with theoretical particle and nuclear physics. The Bell Telephone Laboratories was one of the first institutes to conduct a research program in condensed matter physics. References to "condensed" state can be traced to earlier sources. As a matter of fact, it would be more correct to unify them under the title of'condensed bodies'". One of the first studies of condensed states of matter was by English chemist Humphry Davy, in the first decades of the nineteenth century. Davy observed that of the forty chemical elements known at the time, twenty-six had metallic properties such as lustre, ductility and high electrical and thermal conductivity. This indicated that the atoms in Dalton's atomic theory were not indivisible as Dalton claimed, but had inner structure. By 1908, James Dewar and H. Kamerlingh Onnes were successfully able to liquefy hydrogen and then newly discovered helium, respectively. Paul Drude in 1900 proposed the first theoretical model for a classical electron moving through a metallic solid. The phenomenon completely surprised the best theoretical physicists of the time, it remained unexplained for several decades. Drude's classical model was augmented by Wolfgang Pauli, Arnold Sommerfeld, Felix Bloch and other physicists.
Condensed matter physics
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Heike Kamerlingh Onnes and Johannes van der Waals with the helium "liquefactor" in Leiden (1908)
Condensed matter physics
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Condensed matter physics
Condensed matter physics
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A replica of the first point-contact transistor in Bell labs
Condensed matter physics
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Computer simulation of "nanogears" made of fullerene molecules. It is hoped that advances in nanoscience will lead to machines working on the molecular scale.
233.
Scalar field
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In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a physical quantity. Examples used in physics include the temperature distribution throughout space, spin-zero quantum fields, such as the Higgs field. These fields are the subject of scalar theory. Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U. Physically, a scalar field is additionally distinguished by having units of measurement associated with it. More subtly, scalar fields are often contrasted with pseudoscalar fields. In physics, scalar fields often describe the potential energy associated with a particular force. The force is a field, which can be obtained as the gradient of the potential energy scalar field. Examples include: Potential fields, such as the electric potential in electrostatics, are scalar fields which describe the more familiar forces. A temperature, humidity or field, such as those used in meteorology. In quantum theory, a scalar field is associated with spin-0 particles. The field may be real or complex valued. Complex scalar fields represent charged particles. These include the charged Higgs field of the Standard Model, well as the charged pions mediating the strong nuclear interaction.
Scalar field
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A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of color.
234.
Quantum field theory
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QFT treats particles as excited states of the physical field, so these are called field quanta. In quantum theory, quantum mechanical interactions among particles are described by interaction terms among the corresponding underlying quantum fields. These interactions are conveniently visualized by Feynman diagrams, which are a formal tool of relativistically covariant theory, serving to evaluate particle processes. The first achievement of namely quantum electrodynamics, is "still the paradigmatic example of a successful quantum field theory". Ordinarily, quantum mechanics cannot give an account of photons which constitute the prime case of relativistic ‘particles’. The formalism of QFT is needed for an explicit description of photons. However, quantum mechanics did not focus much on problems of radiation. As as the conceptual framework of quantum mechanics was developed, a small group of theoreticians tried to extend quantum methods to electromagnetic fields. A good example is the famous paper by Born, Jordan & Heisenberg. The ideas of QM were thus extended to systems having an infinite number of degrees of freedom, so an infinite array of quantum oscillators. The inception of QFT is usually considered to be Dirac's famous 1927 paper on "The theory of the emission and absorption of radiation". Here Dirac coined the name "electrodynamics" for the part of QFT, developed first. Employing the theory of the quantum oscillator, Dirac gave a theoretical description of how photons appear in the quantization of the electromagnetic radiation field. Later, Dirac's procedure became a model for the quantization of other fields well. These first approaches to QFT were further developed during the following three years.
Quantum field theory
235.
Minkowski space
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Minkowski space is closely associated with Einstein's theory of special relativity, is the most common mathematical structure on which special relativity is formulated. Because it treats time differently than it treats the three spatial dimensions, Minkowski space differs from four-dimensional Euclidean space. In 3-dimensional Euclidean space, the isometry group is the Euclidean group. It consists of rotations, reflections, translations. All Galilean transformations preserve the 3-dimensional Euclidean distance. This distance is purely spatial. Time differences are separately preserved as well. This changes in the spacetime of special relativity, where space and time are interwoven. Spacetime is equipped with a non-positive definite non-degenerate bilinear form. Equipped with this inner product, the mathematical model of spacetime is called Minkowski space. The analogue of the Galilean group for Minkowski space, preserving the spacetime interval is the Poincaré group. In summary, Galilean spacetime and Minkowski spacetime are, when viewed as barebones manifolds, actually the same. They differ in what kind of further structures are defined on them. Here the speed of light c is, following Poincare, set to unity. The naming and ordering of coordinates, with the same labels for space coordinates, but with the imaginary time coordinate as the fourth coordinate, is conventional.
Minkowski space
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Hermann Minkowski (1864 – 1909) was a German mathematician. He found that the theory of special relativity, introduced by his former student Albert Einstein, could best be understood in a four-dimensional space, since known as the Minkowski spacetime.
236.
Complex number
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In this expression, b is the imaginary part of the complex number. A + bi can be identified with the point in the complex plane. As as their use within mathematics, complex numbers have practical applications in many fields, including physics, chemistry, biology, economics, electrical engineering, statistics. The Italian mathematician Gerolamo Cardano is the first known to have introduced complex numbers. He called them "fictitious" during his attempts to find solutions to cubic equations in the 16th century. Complex numbers allow solutions to certain equations that have no solutions in real numbers. For example, the equation = − 9 has no real solution, since the square of a real number can not be negative. Complex numbers provide a solution to this problem. According to the fundamental theorem of algebra, all polynomial equations with complex coefficients in a single variable have a solution in complex numbers. For example, 3.5 + 2i is a complex number. By this convention the imaginary part does not include the imaginary unit: hence b, not bi, is the imaginary part. For example, Re = − 3.5 Im = 2. Hence, in imaginary parts, a complex number z is equal to Re + Im ⋅ i. This expression is sometimes known as the Cartesian form of z. A can be regarded as a complex number a + 0i whose imaginary part is 0.
Complex number
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A complex number can be visually represented as a pair of numbers (a, b) forming a vector on a diagram called an Argand diagram, representing the complex plane. "Re" is the real axis, "Im" is the imaginary axis, and i is the imaginary unit which satisfies i 2 = −1.
237.
Particle decay
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Particle decay is the spontaneous process of one unstable subatomic particle transforming into multiple other particles. The particles created in this process must each be less massive than the original, although the total mass of the system must be conserved. A particle is unstable if there is at least one allowed final state that it can decay into. Unstable particles will often have multiple ways of decaying, each with its own associated probability. Decays are mediated by several fundamental forces. The particles in the final state may themselves be subject to further decay. Note that this article uses natural units, where c = ℏ = 1. All data is from the Particle Data Group. The lifetime of a particle is given by the inverse of Γ, the probability per unit time that the particle will decay. One may integrate over the space to obtain the total decay rate for the specified final state. The branching ratio for each mode is given by its rate divided by the full decay rate. Say a particle of mass M decays into two particles, labeled 1 and 2. Also, in spherical coordinates, d 3 p → = | p → | 2 d | p → | d ϕ d. When the imaginary part is large compared to the real part, the particle is usually thought of as a resonance more than a particle. For a particle of mass M + i Γ, the particle decays after time of order of 1 / Γ.
Particle decay
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...while in the Lab Frame the parent particle is probably moving at a speed close to the speed of light so the two emitted particles would come out at angles different from those in the center of momentum frame.
238.
Eigenvalue
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There is a correspondence between n by n square matrices and linear transformations from an n-dimensional vector space to itself. For this reason, it is equivalent to define eigenvalues and eigenvectors using either the language of matrices or the language of linear transformations. If the eigenvalue is negative, the direction is reversed. Eigenvalues and eigenvectors feature prominently in the analysis of linear transformations. The prefix eigen- is adopted from the German word eigen for "proper", "inherent"; "own", "individual", "special"; "specific", "peculiar", or "characteristic". In essence, an eigenvector v of a linear transformation T is a non-zero vector that, when T is applied to it, does not change direction. Applying T to the eigenvector only scales the eigenvector by the scalar value λ, called an eigenvalue. This condition can be written as the equation T = λ v, referred to as the eigenvalue equation or eigenequation. In general, λ may be any scalar. For example, λ may be negative, in which case the eigenvector reverses direction as part of the scaling, or it may be zero or complex. The Mona Lisa example pictured at right provides a simple illustration. Each point on the painting can be represented as a vector pointing from the center of the painting to that point. The linear transformation in this example is called a shear mapping. The vectors pointing to each point in the original image are therefore tilted right or left and made longer or shorter by the transformation. Notice that points along the horizontal axis do not move at all when this transformation is applied.
Eigenvalue
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In this shear mapping the red arrow changes direction but the blue arrow does not. The blue arrow is an eigenvector of this shear mapping because it doesn't change direction, and since its length is unchanged, its eigenvalue is 1.
239.
Resonance
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Frequencies at which the amplitude is a relative maximum are known as the system's resonant frequencies or resonance frequencies. At resonant frequencies, periodic driving forces have the ability to produce large amplitude oscillations, due to the storage of vibrational energy. Resonance occurs when a system is able to easily transfer energy between two or more different storage modes. However, there are some losses to cycle called damping. When damping is small, the resonant frequency is approximately equal to the natural frequency of the system, a frequency of unforced vibrations. Some systems have multiple, resonant frequencies. Resonant systems can be used to pick out specific frequencies from a complex vibration containing many frequencies. Resonance is exploited in many manmade devices. It is the mechanism by which virtually all sinusoidal vibrations are generated. Many sounds we hear, such as when hard objects of metal, wood are struck, are caused by brief resonant vibrations in the object. Other short wavelength electromagnetic radiation is produced by resonance on an atomic scale, such as electrons in atoms. It may cause violent swaying motions and even catastrophic failure in improperly constructed structures including bridges, trains, aircraft. Avoiding resonance disasters is a major concern in every building, bridge construction project. As a countermeasure, shock mounts can be installed to thus dissipate the absorbed energy. The Taipei 101 building relies on a 660-tonne pendulum -- a tuned damper -- to cancel resonance.
Resonance
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Pushing a person in a swing is a common example of resonance. The loaded swing, a pendulum, has a natural frequency of oscillation, its resonant frequency, and resists being pushed at a faster or slower rate.
Resonance
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NMR Magnet at HWB-NMR, Birmingham, UK. In its strong 21.2- tesla field, the proton resonance is at 900 MHz.
240.
Square root
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For example, 4 and 4 are square roots of 16 because 42 = 2 = 16. For example, the square root of 9 is 3, denoted √ 9 = 3, because 32 = 3 × 3 = 9 and 3 is non-negative. The term whose root is being considered is known as the radicand. The radicand is the expression underneath the radical sign, in this example 9. A has two square roots: √ a, positive, − √ a, negative. Together, these two roots are denoted ± √a. For positive a, the principal square root can also be written in exponent notation, as a1/2. Square roots of negative numbers can be discussed within the framework of complex numbers. A method for finding very good approximations to the square roots of 3 are given in the Baudhayana Sulba Sutra. Aryabhata in the Aryabhatiya, has given a method for finding the square root of numbers having many digits. This is the theorem Euclid X, 9 almost certainly due to Theaetetus dating back to 380 BC. The particular case √ 2 is traditionally attributed to Hippasus. It is exactly the length of the diagonal of a square with length 1. A 9th-century Indian mathematician, was the first to state that square roots of negative numbers do not exist. A symbol for square roots, written as an elaborate R, was invented by Regiomontanus.
Square root
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First leaf of the complex square root
Square root
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The mathematical expression 'The (principal) square root of x"
241.
Real number
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In mathematics, a real number is a value that represents a quantity along a line. The adjective real in this context was introduced by Descartes, who distinguished between real and imaginary roots of polynomials. The real numbers include all the rational numbers, such as the fraction 4/3, all the irrational numbers, such as √ 2. Included within the irrationals are the transcendental numbers, such as π. Complex numbers include real numbers. These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. All these definitions are thus equivalent. Around 500 BC, the Greek mathematicians led by Pythagoras realized the need in particular the irrationality of the square root of 2. Arabic mathematicians merged the concepts of "number" and "magnitude" into a more general idea of real numbers. In the 17th century, Descartes introduced the term "real" to describe roots of a polynomial, distinguishing them from "imaginary" ones. In the 19th centuries, there was much work on irrational and transcendental numbers. Évariste Galois developed techniques for determining whether a given equation could be solved by radicals, which gave rise to the field of Galois theory. Charles Hermite first proved that e is transcendental, Ferdinand von Lindemann, showed that π is transcendental. Lindemann's proof has finally been made elementary by Adolf Hurwitz and Paul Gordan. The development of calculus in the 18th century used the entire set of real numbers without having defined them cleanly.
Real number
–
A symbol of the set of real numbers (ℝ)
242.
Dark energy
–
Dark energy is the most accepted hypothesis to explain the observations since the 1990s indicating that the universe is expanding at an accelerating rate. The mass–energy of dark matter and ordinary matter contribute 26.8% and 4.9%, respectively, other components such as neutrinos and photons contribute a very small amount. However, it comes to dominate the mass–energy of the universe because it is uniform across space. Contributions from scalar fields that are constant in space are usually also included in the constant. The cosmological constant can be formulated to be equivalent to the zero-point radiation of space i.e. the energy. Scalar fields that do change in space can be difficult to distinguish from a constant because the change may be extremely slow. High-precision measurements of the expansion of the universe are required to understand how the rate changes over time and space. In general relativity, the evolution of the rate is parameterized by the cosmological equation of state. Measuring the equation of state for dark energy is one of the biggest efforts in observational today. Dark energy has been used as a crucial ingredient in a recent attempt to formulate a cyclic model for the universe. Many things about the nature of dark energy remain matters of speculation. The theoretical need for a type of additional energy, not dark matter to form the observationally flat universe. It can be inferred from measures of large scale wave-patterns of mass density in the universe. Dark energy is not known to interact through any of the fundamental forces other than gravity. Since it is quite rarefied — roughly 10−27 kg/m3 — it is unlikely to be detectable in laboratory experiments.
Dark energy
–
Diagram representing the accelerated expansion of the universe due to dark energy.
Dark energy
–
A Type Ia supernova (bright spot on the bottom-left) near a galaxy
Dark energy
–
The equation of state of Dark Energy for 4 common models by Redshift. A: CPL Model, B: Jassal Model, C: Barboza & Alcaniz Model, D: Wetterich Model
243.
Radiation
–
In physics, radiation is the emission or transmission of energy in the form of waves or particles through space or through a material medium. Radiation is often categorized as either ionizing or non-ionizing depending on the energy of the radiated particles. Ionizing radiation carries more than 10 eV, enough to ionize atoms and molecules, break chemical bonds. This is an important distinction due to the large difference in harmfulness to living organisms. A common source of ionizing radiation is radioactive materials that emit γ radiation, consisting of helium nuclei, electrons or positrons, photons, respectively. The higher energy range of ultraviolet light constitute the ionizing part of the electromagnetic spectrum. This type of radiation only damages cells if the intensity is high enough to cause excessive heating. Ultraviolet radiation has some features of both ionizing and non-ionizing radiation. These properties derive from ultraviolet's power to alter chemical bonds, even without having quite enough energy to ionize atoms. The word radiation arises from the phenomenon of waves radiating from a source. This aspect leads to a system of measurements and physical units that are applicable to all types of radiation. This law does not apply close to an extended source of radiation or for focused beams. Radiation with sufficiently high energy can ionize atoms;, to say it can knock electrons off atoms and create ions. Ionization occurs when an electron is stripped from an shell of the atom, which leaves the atom with a positive charge. Thus "ionizing radiation" is somewhat artificially separated from particle radiation and electromagnetic radiation, simply due to its great potential for biological damage.
Radiation
–
Illustration of the relative abilities of three different types of ionizing radiation to penetrate solid matter. Typical alpha particles (α) are stopped by a sheet of paper, while beta particles (β) are stopped by an aluminium plate. Gamma radiation (γ) is damped when it penetrates lead. Note caveats in the text about this simplified diagram.
244.
Negative pressure
–
Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure. Various units are used to express pressure. Pressure is the amount of force acting per area. The symbol for it is P. The IUPAC recommendation for pressure is a lower-case p. However, upper-case P is widely used. Mathematically: p = F A where: p is the pressure, F is the normal force, A is the area of the surface on contact. Pressure is a quantity. It relates the vector element with the normal force acting on it. It is incorrect to say "the pressure is directed in such direction". The pressure, as a scalar, has no direction. The pressure does not. The pressure remains the same. Pressure is distributed across arbitrary sections of fluid normal to these boundaries or sections at every point. It is conjugate to volume.
Negative pressure
–
Mercury column
Negative pressure
–
Pressure as exerted by particle collisions inside a closed container.
Negative pressure
–
The effects of an external pressure of 700bar on an aluminum cylinder with 5mm wall thickness
Negative pressure
–
low pressure chamber in Bundesleistungszentrum Kienbaum, Germany
245.
Effective mass (solid-state physics)
–
For some materials, the effective mass can be considered to be a simple constant of a material. In general, however, the value of effective mass depends on the purpose for which it can vary depending on a number of factors. For electrons or electron holes in a solid, the effective mass is usually stated in units of the true mass of me. As a result, the mass in models such as the Drude model must be replaced with the effective mass. One remarkable property is that the effective mass can become negative, when the band curves downwards away from a maximum. This explains the existence of the positive-charge, positive-mass quasiparticles that can be found in semiconductors. In any case, if the structure has the simple parabolic form described above, then the value of effective mass is unambiguous. Unfortunately, this parabolic form is not valid for describing most materials. In complex materials there is no single definition of "effective mass" but instead multiple definitions, each suited to a particular purpose. The rest of the article describes these effective masses in detail. The offsets k0, k0, y, k0, z reflect that the conduction band minimum is no longer centered at zero wavevector. Still, in crystals such as silicon the overall properties such as conductivity appear to be isotropic. This is because there are multiple valleys, each with effective masses rearranged along different axes. The valleys collectively act together to give an isotropic conductivity. It is possible to average the different axes' effective masses together in some way, to regain the free picture.
Effective mass (solid-state physics)
–
Constant energy ellipsoids in silicon near the six conduction band minima. For each valley (band minimum), the effective masses are m ℓ = 0.92 m e ("longitudinal"; along one axis) and m t = 0.19 m e ("transverse"; along two axes).
Effective mass (solid-state physics)
–
Bulk band structure for Si,Ge,GaAs and InAs generated with tight binding model. Note that Si and Ge are indirect with minima at X and L, while GaAs and InAs are direct band gap materials.
246.
International System of Quantities
–
The International System of Quantities is a system based on seven base quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, luminous intensity. Other quantities such as area, electrical resistance are derived from these base quantities by clear, non-contradictory equations. The ISQ also includes many other quantities in modern science and technology. The ISQ was finalised in 2009 with the publication of ISO 80000-1. The 14 parts of ISO/IEC 80000 define quantities used in scientific disciplines such as mechanics, light, acoustics, electromagnetism, information technology, chemistry, physiology. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics. The dimension of a physical quantity does not include magnitude or units. The symbolic representation of the dimension of a base quantity is a single upper-case letter in roman sans-serif type. A derived quantity is a quantity in a system of quantities, a defined in terms of the base quantities of that system. The ISQ defines derived quantities. The symbol may be omitted if its exponent is zero. In the ISQ, the quantity dimension of velocity is denoted L T − 1. The following table lists some quantities defined by the ISQ. A quantity of dimension one is historically known as a dimensionless quantity, all its dimension symbol is 1.
International System of Quantities
–
Base quantity
247.
Avogadro constant
–
Thus, it is the proportionality factor that relates the molar mass of a compound to the mass of a sample. Avogadro's constant, often designated with L, has the value 7023602214085700000 − 1 in the International System of Units. This number is also known as Loschmidt constant in German literature. For instance, to a first approximation, 1 gram of hydrogen element, having the atomic number 1, has 7023602200000000000♠6.022×1023 hydrogen atoms. Similarly, 12 grams of 12C, with the mass number 12, has the same number of carbon atoms, 7023602200000000000♠6.022×1023. Avogadro's number is a dimensionless quantity, has the same numerical value of the Avogadro constant given in base units. In contrast, the Avogadro constant has the dimension of reciprocal amount of substance. Revisions in the base set of SI units necessitated redefinitions of the concepts of chemical quantity. Avogadro's number, its definition, was deprecated in favor of the Avogadro constant and its definition. The French physicist Jean Perrin in 1909 proposed naming the constant in honor of Avogadro. Perrin won the 1926 Nobel Prize in Physics, largely for his work in determining the Avogadro constant by several different methods. Accurate determinations of Avogadro's number require the measurement of a single quantity on both the atomic and macroscopic scales using the same unit of measurement. This became possible for the first time when American physicist Robert Millikan measured the charge on an electron in 1910. By dividing the charge on a mole of electrons by the charge on a single electron the value of Avogadro's number is obtained. Since 1910, newer calculations have more accurately determined the values for the Faraday constant and the elementary charge.
Avogadro constant
–
Amedeo Avogadro
Avogadro constant
–
Achim Leistner at the Australian Centre for Precision Optics (ACPO) holding a one-kilogram single-crystal silicon sphere for the International Avogadro Coordination.
248.
University of Chicago Press
–
The University of Chicago Press is the largest and one of the oldest university presses in the United States. One of its quasi-independent projects is a digital repository for scholarly books. The Press building is located south of the Midway Plaisance on the University of Chicago campus. The University of Chicago Press was founded in 1891, making one of the oldest continuously operating university presses in the United States. Its first published book was Robert F. Harper's Assyrian and Babylonian Letters Belonging of the British Museum. For its first three years, the Press was an entity discrete from the university; it was operated by the Boston publishing house D. C. Heath in conjunction with the Chicago printer R. R. Donnelley. In 1894 the university officially assumed responsibility for the Press. As part of the university, the Press started working on the Decennial Publications. This allowed the Press, by 1905, to begin publishing books by scholars not of the University of Chicago. By 1931, the Press was an established, academic publisher. In 1956, the Press first published paperback-bound books under its imprint. Of the Press's best-known books, most date from the 1950s, including Richmond Lattimore's The Iliad of Homer. In 1966, Morris Philipson began his thirty-four-year tenure as director of the University of Chicago Press. As the Press's scholarly volume expanded, the Press also advanced as a publisher.
University of Chicago Press
–
University of Chicago Press
249.
International Standard Book Number
–
The International Standard Book Number is a unique numeric commercial book identifier. An ISBN is assigned to each variation of a book. For example, an e-book, a hardcover edition of the same book would each have a different ISBN. The ISBN is 13 digits long if assigned after 1 January 2007, 10 digits long if assigned before 2007. The method of assigning an ISBN varies from country to country, often depending on how large the publishing industry is within a country. The initial ISBN configuration of recognition was generated based upon the 9-digit Standard Book Numbering created in 1966. The 10-digit ISBN format was published in 1970 as international standard ISO 2108. The International Standard Serial Number, identifies periodical publications such as magazines; and the International Standard Music Number covers for musical scores. The ISBN configuration of recognition was generated in 1967 in the United Kingdom by Emery Koltay. The 10-digit ISBN format was published as international standard ISO 2108. The United Kingdom continued to use the 9-digit SBN code until 1974. The ISO on-line facility only refers back to 1978. An SBN may be converted by prefixing the digit "0". This can be converted to ISBN 0-340-01381-8; the digit does not need to be re-calculated. Since 1 ISBNs have contained 13 digits, a format, compatible with "Bookland" European Article Number EAN-13s.
International Standard Book Number
–
A 13-digit ISBN, 978-3-16-148410-0, as represented by an EAN-13 bar code
250.
Oxford University Press
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Oxford University Press is the largest university press in the world, the second oldest after Cambridge University Press. They are headed to the delegates, who serves as OUP's chief executive and as its major representative on other university bodies. Oxford University has used a similar system to oversee OUP since the 17th century. The university grew into a major printer of Bibles, prayer books, scholarly works. OUP took on the project that expanded to meet the ever-rising costs of the work. Moves into international markets led to OUP opening its own offices outside the United Kingdom, beginning with New York City in 1896. By contracting out binding operations, the modern OUP publishes some 6,000 new titles around the world each year. OUP was first exempted from United Kingdom corporation tax in 1978. The Oxford University Press Museum is located on Oxford. Visits are led by a member of the archive staff. Displays include a 19th-century printing press, the printing and history of the Oxford Almanack, Alice in Wonderland and the Oxford English Dictionary. The first printer associated with Oxford University was Theoderic Rood. An edition of Rufinus's Expositio in symbolum apostolorum, was printed by another, anonymous, printer. Famously, this was mis-dated in Roman numerals as "1468", thus apparently pre-dating Caxton. Rood's printing included John Ankywyll's Compendium totius grammaticae, which set new standards for teaching of Latin grammar.
Oxford University Press
–
Oxford University Press on Walton Street.
Oxford University Press
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2008 conference booth
251.
Scientific American
–
Scientific American is an American popular science magazine. Many famous scientists, including Albert Einstein, have contributed articles in the past 170 years. It is the oldest continuously published monthly magazine in the United States. Scientific American was founded by publisher Rufus M. Porter as a four-page weekly newspaper. Throughout its early years, much emphasis was placed on reports of what was going on at the U.S. Patent Office. Current issues include a "this date in history" section, featuring excerpts from articles originally published 50, 100, 150 years earlier. Topics include noteworthy advances in the history of science and technology. Porter sold the publication to Alfred Ely Beach and Orson Desaix Munn I a mere ten months after founding it. Until 1948, it remained owned by Munn & Company. Under Orson Desaix Munn III, grandson of Orson I, it had evolved into something of a "workbench" publication, similar to the twentieth-century incarnation of Popular Science. In the years after World War II, the magazine fell into decline. Thus the partners -- general manager Donald H. Miller, Jr. -- essentially created a new magazine. Miller retired in 1984 when Gerard Piel's Jonathan became president and editor; circulation had grown fifteen-fold since 1948. In 1986, it was sold to the Holtzbrinck group of Germany, which has owned it since.
Scientific American
–
Cover of the March 2005 issue
Scientific American
–
PDF of first issue: Scientific American Vol. 1, No. 01 published August 28, 1845
Scientific American
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Special Navy Supplement, 1898
252.
Dialogue Concerning the Two Chief World Systems
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The Dialogue Concerning the Two Chief World Systems is a 1632 Italian-language book by Galileo Galilei comparing the Copernican system with the traditional Ptolemaic system. It was translated into Latin by Matthias Bernegger. The book was dedicated to Ferdinando II de' Medici, Grand Duke of Tuscany, who received the first printed copy on February 22, 1632. In the Copernican system, other planets orbit the Sun, while in the Ptolemaic system, everything in the Universe circles around the Earth. The Dialogue was published under a formal license from the Inquisition. As a result, the formal title on the page is Dialogue, followed by Galileo's name, academic posts, followed by a long subtitle. This must be kept in mind when discussing Galileo's motives for writing the book. Although the book is presented formally as a consideration of both systems, there is no question that the Copernican side gets the better of the argument. He is named after Galileo's friend Filippo Salviati. Sagredo is an intelligent layman, initially neutral. He is named after Galileo's friend Giovanni Francesco Sagredo. A dedicated follower of Ptolemy and Aristotle, presents the traditional views and the arguments against the Copernican position. Colombe was the leader of a group of Florentine opponents of Galileo's, which some of the latter's friends referred as "the pigeon league". The discussion ranges over much of contemporary science. Some of this is to show what Galileo considered good science, on magnetism.
Dialogue Concerning the Two Chief World Systems
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A copy of The Dialogo, Florence edition, located at the Tom Slick rare book collection at Southwest Research Institute, in Texas.
Dialogue Concerning the Two Chief World Systems
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Frontispiece and title page of the Dialogue, 1632
Dialogue Concerning the Two Chief World Systems
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Actual path of cannonball B is from C to D
253.
House of Elzevir
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Elzevir is the name of a celebrated family of Dutch booksellers, publishers, printers of the 17th and early 18th centuries. The duodecimo series of "Elzevirs" became very desirable among bibliophiles, who sought to obtain the tallest and freshest copies of these tiny books. A contemporary publisher Elsevier takes its name from this early modern business. Although he worked throughout his life, Louis seems to have worked mostly as a bookbinder in his early decades. In 1580, he made a final move to Leiden, where he seems to have worked first as a bookbinder, later as a publisher. In all Louis published about 150 works. He died on 4 February 1617. Of his seven sons, Matthieu/Matthijs, Louis, Gilles, Joost and Bonaventura, adopted their father's profession. Among them Bonaventura Elzevir is the most celebrated. He began business as a publisher in 1608, in 1626 took into partnership Abraham Elzevir, a son of Matthijs, born at Leiden in 1592. Bonaventura about a month afterwards. The fame of the Elzevir editions rests chiefly on the works issued by the firm of Bonaventure and Abraham. After its dissolution Jean carried on the business alone until his death in 1661. In 1654 Daniel joined his cousin Louis, born in 1604, had established a printing press at Amsterdam in 1638. Daniel in 1680.
House of Elzevir
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Book about fencing published in Leiden by Isack Elsevier in 1619
House of Elzevir
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Elsevir printer mark depicted in the Library of Congress
254.
Cambridge University Press
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Cambridge University Press is the publishing business of the University of Cambridge. Granted letters patent in 1534, Cambridge University is the world's oldest publishing house and the second-largest university press in the world. Cambridge University also holds letters patent as the Queen's Printer. Cambridge University Press is both an academic and educational publisher. With a global sales presence, offices in more than 40 countries, Cambridge University publishes over 50,000 titles by authors from over 100 countries. Its publishing includes academic journals, monographs, reference works, English-language teaching and learning publications. Cambridge University Press is a charitable enterprise that transfers part of its annual surplus back to the university. Cambridge University Press is both the oldest house in the world and the oldest university press. Cambridge is one of the two privileged presses. Authors published by Cambridge have included John Milton, William Harvey, Isaac Newton, Stephen Hawking. In 1591, John Legate, printed the first Cambridge Bible, an octavo edition of the popular Geneva Bible. The London Stationers objected strenuously, claiming that they had the monopoly on Bible printing. The university's response was to point out the provision in its charter to print'all manner of books'. Cambridge University was in 1698, that a body of senior scholars was appointed to be responsible to the university for the Press's affairs. Its role still includes the review and approval of the Press's planned output.
Cambridge University Press
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The University Printing House, on the main site of the Press
Cambridge University Press
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The letters patent of Cambridge University Press by Henry VIII allow the Press to print "all manner of books". The fine initial with the king's portrait inside it and the large first line of script are still discernible.
Cambridge University Press
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The Pitt Building in Cambridge, which used to be the headquarters of Cambridge University Press, and now serves as a conference centre for the Press.
Cambridge University Press
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On the main site of the Press
255.
ArXiv
–
In many fields of physics, almost all scientific papers are self-archived on the arXiv repository. Begun on August 1991, arXiv.org passed the half-million article milestone on October 3, 2008, hit a million by the end of 2014. By 2014 the rate had grown to more than 8,000 per month. The arXiv was made possible by the low-bandwidth TeX format, which allowed scientific papers to be easily transmitted over the Internet and rendered client-side. The number of papers being sent soon filled mailboxes to capacity. Additional modes of access were soon added the World Wide Web in 1993. The e-print was quickly adopted to describe the articles. Its original name was xxx.lanl.gov. It is now hosted principally with 8 mirrors around the world. Its existence was one of the precipitating factors that led to the current movement in scientific publishing known as open access. Scientists regularly upload their papers to arXiv.org for worldwide access and sometimes for reviews before they are published in peer-reviewed journals. Ginsparg was awarded a MacArthur Fellowship in 2002 for his establishment of arXiv. Annual donations were envisaged to vary in size between $2,300 to $4,000, based on each institution’s usage. In September 2011, Cornell University Library took overall financial responsibility for arXiv's operation and development. Ginsparg was quoted in the Chronicle of Higher Education as saying it "was supposed to be a three-hour tour, not a sentence".
ArXiv
–
arXiv
ArXiv
–
A screenshot of the arXiv taken in 1994, using the browser NCSA Mosaic. At the time, HTML forms were a new technology.
256.
American Journal of Physics
–
The American Journal of Physics is a monthly, peer-reviewed scientific journal published by the American Association of Physics Teachers and the American Institute of Physics. The editor is David P. Jackson of Dickinson College. The focus of this journal is undergraduate and graduate physics. The intended audience is college and physics teachers and students. Coverage includes current research in related topics, instructional laboratory equipment, laboratory demonstrations, teaching methodologies, lists of resources, book reviews. In addition, historical, cultural aspects of physics are also covered. The former title of this journal was American Physics Teacher. It was then a bimonthly from 1937 to 1939. After volume 7 was published in December 1939, the name of the journal was changed to its current title in February 1940. Hence, the publication begins with volume 8 in February 1940. Science Abstracts. Series A European Journal of Physics American Journal of Physics American Journal of Physics editor's website
American Journal of Physics
–
American Journal of Physics
257.
Perseus Books
–
Perseus Books Group was an American publishing company founded in 1996 by investor Frank Pearl. In April 2016, its business was acquired by Hachette Book Group and its distribution business by Ingram Content Group. After the death of Frank Pearl, Perseus was sold to a private equity firm. The Perseus Books Group currently has 12 imprints: Before Avalon Publishing Group was integrated into the Perseus Books Group, it published on 14 imprint presses. In 2007, some of these imprints were integrated into the Perseus Books Group, while others were sold to other companies. Perseus also sold one of their imprints in the process. Publishers Group West, founded in 1976, based in Berkeley, California. Consortium Book Sales and Distribution, founded in 1985, based in Minnesota. Perseus Distribution, founded in 1999, based in New York City. Legato Publishers Group, founded in 2013, based in Chicago. Perseus Books Group
Perseus Books
–
Perseus Books Group
258.
Wikisource
–
Wikisource is an online digital library of free content textual sources on a wiki, operated by the Wikimedia Foundation. The project's aims are to host all forms of free text, in many languages, translations. Originally conceived as an archive to store important historical texts, it has expanded to become a general-content library. The project officially began under the name Project Sourceberg. It received its own domain name seven months later. It is also cited by organisations such as the National Archives and Records Administration. Verification was initially made offline, or by trusting the reliability of digital libraries. Now works are supported by online scans via the ProofreadPage extension, which ensures the accuracy of the project's texts. Each representing a specific language, now only allow works backed up with scans. While the bulk of its collection are texts, Wikisource as a whole hosts other media, to audio books. Some Wikisources allow user-generated annotations, subject to the specific policies of the Wikisource in question. Wikisource's early history included the move to language subdomains in 2005. The original concept for Wikisource was as storage for important historical texts. These texts were intended to support Wikipedia articles, as an archive in its own right. The collection was initially focused on important cultural material, distinguishing it from other digital archives such as Project Gutenberg.
Wikisource
–
The original Wikisource logo
Wikisource
–
Screenshot of wikisource.org home page
Wikisource
–
::: Original text
Wikisource
–
::: Action of the modernizing tool
259.
Frank Wilczek
–
Frank Anthony Wilczek is an American theoretical physicist, mathematician and a Nobel laureate. Wilczek is currently the Herman Feshbach Professor of Physics at the Massachusetts Institute of Technology, well as full Professor at Stockholm University. Wilczek is on the Scientific Advisory Board for the Future of Life Institute. Born in New York, of Polish and Italian origin, he was educated in the public schools of Queens, attending Martin Van Buren High School. It was as a result of Frank Wilczek having been administered an IQ test. Wilczek was raised Catholic. He holds the Herman Feshbach Professorship of Physics at MIT Center for Theoretical Physics. He became a foreign member of the Royal Netherlands Academy of Arts and Sciences in 2000. Wilczek was awarded the Lorentz Medal in 2002. He won the Lilienfeld Prize of the American Physical Society in 2003. In the same year Wilczek was awarded the Faculty of Mathematics and Physics Commemorative Medal from Charles University in Prague. Wilczek was Particle Physics Prize of the European Physical Society. He was also the co-recipient for Science. On January 2013 he received an honorary doctorate from the Faculty of Science and Technology at Uppsala University, Sweden. Wilczek currently serves for Science & the Public.
Frank Wilczek
–
Frank Wilczek
260.
John Baez
–
John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside in Riverside, California. He is known on spin foams in loop quantum gravity. For some time, his research had focused to physics and other things. It now has a following in its new form, the blog "Azimuth". This Week's Finds anticipated the concept of a personal weblog. Additionally, Baez is known as the author of the crackpot index. Baez was born in California. He graduated from Princeton University in Princeton, New Jersey, in mathematics in 1982. In 1986, he graduated from the Massachusetts Institute of Technology in Cambridge, Massachusetts, under the direction of Irving Segal. After a post-doctoral period at Yale University in Connecticut, he has been teaching -- since 1989 -- at UC Riverside. Baez is also co-founder of a group blog concerning higher category theory and its applications, as well as its philosophical repercussions. The list of blog authors has extended since. The n-Café community is associated with the nLab wiki and forum, which now run independently of n-Café. It is hosted at Austin's official website. Albert Baez, interested him in physics as a child.
John Baez
–
John C. Baez (August 2009)
261.
SI base unit
–
The International System of Units defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. Other units, such as the litre, are formally not part of the SI, but are accepted with SI. The definitions of the base units have been modified several times since the Metre Convention in 1875, new additions of base units have occurred. However, the candela are linked through their definitions to the mass of the platinum -- iridium cylinder stored in a vault near Paris. Two possibilities have attracted particular attention: the Planck constant and the Avogadro constant. The 23rd CGPM decided to postpone any formal change until the next General Conference in 2011.
SI base unit
–
The seven SI base units and the interdependency of their definitions: for example, to extract the definition of the metre from the speed of light, the definition of the second must be known while the ampere and candela are both dependent on the definition of energy which in turn is defined in terms of length, mass and time.
262.
Length
–
In geometric measurements, length is the most extended dimension of an object. In the International System of Quantities, length is any quantity with distance. In other contexts "length" is the measured dimension of an object. For example, it is possible to cut a length of a wire, shorter than thickness. Volume is a measure of three dimensions. In most systems of measurement, the unit of length is a unit, from which other units are defined. Measurement has been important ever since humans started using building materials, occupying land and trading with neighbours. As society has become more technologically oriented, much higher accuracies of measurement are required from micro-electronics to interplanetary ranging. This added together to make longer units like the stride. The cubit could vary considerably due to the different sizes of people. After Albert Einstein's special relativity, length can longer be thought of being constant in all reference frames. This means length of an object is variable depending on the observer. In the physical sciences and engineering, when one speaks of "units of length", the word "length" is synonymous with "distance". There are several units that are used to measure length. In the International System of Units, the basic unit of length is now defined in terms of the speed of light.
Length
–
Base quantity
263.
Metre
–
The metre, or meter, is the base unit of length in the International System of Units. The SI symbol is m. The metre is defined as the distance travelled in a vacuum in 1/299 792 458 seconds. The metre was originally defined in 1793 from the equator to the North Pole. In 1799, it was redefined in terms of a prototype bar. In 1960, the metre was redefined in terms of a certain number of wavelengths of a certain line of krypton-86. In 1983, the current definition was adopted. The imperial inch is defined as 0.0254 metres. One metre is about 3 3⁄8 inches longer than a yard, i.e. about 39 3⁄8 inches. Metre is the standard spelling of the Philippines, which use meter. Measuring devices are spelled "-meter" in all variants of English. The suffix" - meter", has the Greek origin as the unit of length. This range of uses is also found in Latin, French, other languages. As a result of the French Revolution, the French Academy of Sciences charged a commission with determining a single scale for all measures. Christiaan Huygens had observed that length to be 39.26 English inches.
Metre
–
Belfry, Dunkirk —the northern end of the meridian arc
Metre
Metre
–
Fortress of Montjuïc —the southerly end of the meridian arc
Metre
–
Creating the metre-alloy in 1874 at the Conservatoire des Arts et Métiers. Present Henri Tresca, George Matthey, Saint-Claire Deville and Debray
264.
Second
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The second is the base unit of time in the International System of Units. It is qualitatively defined as the second division of the hour by sixty being the minute. Seconds may be measured using a mechanical, an atomic clock. SI prefixes are combined with the word second to denote subdivisions of the second, e.g. the millisecond, the microsecond, the nanosecond. Though SI prefixes may also be used to form multiples of the second such as kilosecond, such units are rarely used in practice. The second is also the unit of time in other systems of measurement: the centimetre -- gram -- second, metre -- kilogram -- second, metre -- tonne -- second, foot -- pound -- second systems of units. Absolute zero implies no movement, therefore zero external radiation effects. The second thus defined is consistent with the ephemeris second, based on astronomical measurements. 1⁄. The Hellenistic astronomers Hipparchus and Ptolemy subdivided the day into sixty parts. They also used a mean hour; simple fractions of an hour; and time-degrees. No sexagesimal unit of the day was ever used as an independent unit of time. The modern second is subdivided using decimals - although the third remains in some languages, for example Polish and Turkish. The earliest clocks to display seconds appeared during the last half of the 16th century. The second became accurately measurable to the apparent time displayed by sundials.
Second
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FOCS 1, a continuous cold caesium fountain atomic clock in Switzerland, started operating in 2004 at an uncertainty of one second in 30 million years.
Second
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Key concepts
265.
Electric current
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An electric current is a flow of electric charge. In electric circuits this charge is often carried by moving electrons in a wire. It can also be carried by both ions and electrons such as in a plasma. Electric current is measured using a device called an ammeter. Electric currents cause Joule heating, which creates light in incandescent light bulbs. They also create magnetic fields, which are used in motors, generators. The particles that carry the charge in an electric current are called charge carriers. In metals, one or more electrons from each atom can move freely about within the metal. These conduction electrons are the charge carriers in metal conductors. The conventional symbol for current is I, which originates from the French phrase intensité de courant, meaning current intensity. Current intensity is often referred to simply as current. In a conductive material, the moving charged particles which constitute the electric current are called charge carriers. In other materials, notably the semiconductors, the charge carriers can be negative, depending on the dopant used. Negative charge carriers may even be present at the same time, as happens in an electrochemical cell. The direction of conventional current is arbitrarily defined as the same direction as positive charges flow.
Electric current
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A simple electric circuit, where current is represented by the letter i. The relationship between the voltage (V), resistance (R), and current (I) is V=IR; this is known as Ohm's Law.
266.
Ampere
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The ampere, often shortened to "amp", is the SI unit of electric current and is one of the seven SI base units. It is named after French mathematician and physicist, considered the father of electrodynamics. The ampere is equivalent to one coulomb per second. Amperes are used to express rate of electric charge. The ampere should not be confused with the ampere hour. The coulomb is a unit of charge. The relation of the ampere to the coulomb is the same as that of the watt to the joule. Ampère's law states that there is an attractive or repulsive force between two parallel wires carrying an electric current. The SI unit of charge, the coulomb, "is the quantity of electricity carried in 1 second by a current of 1 ampere". Conversely, a current of one ampere is one coulomb of charge going past a given point per second: 1 A = 1 C s. In general, charge Q is determined by current I flowing for a time t as Q = It. The ampere was originally defined as one tenth of the unit of electric current of units. The size of the unit was chosen so that the units derived in the MKSA system would be conveniently sized. Later, more accurate measurements revealed that this current is 6999999850000000000♠0.99985 A. The proposed change would define 1 A as being the current in the direction of flow of a particular number of elementary charges per second.
Ampere
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Demonstration model of a moving iron ammeter. As the current through the coil increases, the plunger is drawn further into the coil and the pointer deflects to the right.
267.
Thermodynamic temperature
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Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics. Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is zero point. At absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its state, its state of lowest energy. The International System of Units specifies a particular scale for thermodynamic temperature. It selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy. Internal energy may be stored in a number of ways within each way constituting a "degree of freedom". Temperature is vibrations of the particle constituents of matter. These motions comprise the internal energy of a substance. "Translational motions" are always in the classical regime. Translational motions are whole-body movements in three-dimensional space in which particles move about and exchange energy in collisions. Figure 1 below shows translational motion in gases; Figure 4 below shows translational motion in solids. Zero kinetic energy remains in a substance at absolute zero.
Thermodynamic temperature
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Fig. 6 Ice and water: two phases of the same substance
Thermodynamic temperature
Thermodynamic temperature
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Fig. 8 When many of the chemical elements, such as the noble gases and platinum-group metals, freeze to a solid — the most ordered state of matter — their crystal structures have a closest-packed arrangement. This yields the greatest possible packing density and the lowest energy state.
Thermodynamic temperature
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Helium-4, is a superfluid at or below 2.17 kelvins, (2.17 Celsius degrees above absolute zero)
268.
Kelvin
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The kelvin is a unit of measure for temperature based upon an absolute scale. It is assigned the unit K. The kelvin is defined as the fraction 1⁄273.16 of the thermodynamic temperature of the triple point of water. In other words, it is defined such that the triple point of water is exactly 273.16 K. The Kelvin scale is named after Glasgow University engineer and physicist William Lord Kelvin, who wrote for an "absolute thermometric scale". Unlike degree Celsius, the kelvin is not typeset as a degree. The definition implies that absolute zero is equivalent to −273.15 °C. Kelvin calculated that absolute zero was equivalent to −273 °C on the air thermometers of the time. This absolute scale is known today as the Kelvin thermodynamic temperature scale. When spoken, the unit is pluralised using the grammatical rules as for other SI units such as the volt or ohm. When reference is made to the word "kelvin" --, normally a noun -- functions is capitalized. As with most other unit symbols there is a space between the kelvin symbol. Before the 13th CGPM in 1967 -- 1968, the kelvin was called the same as with the other temperature scales at the time. It was distinguished from the other scales with either the adjective suffix "Kelvin" or with "absolute" and its symbol was °K. Before the 13th CGPM, the plural form was "degrees absolute".
Kelvin
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Lord Kelvin, the namesake of the unit
Kelvin
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A thermometer calibrated in degrees Celsius (left) and kelvins (right).
269.
Amount of substance
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Amount of substance is a standards-defined quantity that measures the size of an ensemble of elementary entities, such as atoms, molecules, electrons, other particles. It is sometimes referred to as chemical amount. The International System of Units defines the amount of substance to be proportional to the number of elementary entities present. The SI unit for amount of substance is the mole. It has the mol. The proportionality constant is the inverse of the Avogadro constant. This number has the value 7023602214085700000 ♠ × 1023. Therefore, the amount of substance of a sample is calculated as the mass divided by the mass of the substance. Another unit of amount of substance in use in engineering in the United States is the pound-mole, having the lb-mol. One pound-mole is 7002453592370000000♠453.59237 mol. When quoting an amount of substance, it is necessary to specify the entity involved, unless there is no risk of ambiguity. The simplest way to avoid ambiguity is to replace the term substance by the name of the entity or to quote the empirical formula. The derived quantity in which amount of substance enters into the numerator is amount of c. This name is often abbreviated to concentration, in clinical chemistry where substance concentration is the preferred term to avoid ambiguity with mass concentration. The concentration is incorrect, but commonly used.
Amount of substance
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Base quantity
270.
Mole (unit)
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The mole is the unit of measurement in the International System of Units for amount of substance. This number is expressed by the Avogadro constant, which has a value of 7023602214085700000♠6.022140857×1023 mol−1. The mole has the mol. The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. The mole may also be used to express the number of elementary entities in a given sample of any substance. The concentration of a solution is commonly expressed by its molarity, defined as the number of moles of the dissolved substance per litre of solution. For example, the mean relative molecular mass of natural water is about 18.015, therefore, one mole of water has a mass of about 18.015 grams. The term gram-molecule was formerly used for essentially the same concept. Thus, for example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2. In honor of the unit, some chemists celebrate October 23, a reference to the 1023 scale of the Avogadro constant, as "Mole Day". Some also do the same for February 6 and June 2. Thus, by definition, one mole of pure 12C has a mass of exactly 12 g. It also follows from the definition that X moles of any substance will contain the same number of molecules as X moles of any other substance. The mass per mole of a substance is called its molar mass. The number of elementary entities in a sample of a substance is technically called its amount.
Mole (unit)
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Base units
271.
Luminous intensity
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The SI unit of luminous intensity is an SI base unit. Photometry deals with the measurement of visible light as perceived by human eyes. The human eye has different sensitivities to light of different wavelengths within the spectrum. When adapted for bright conditions, the eye is most sensitive to greenish-yellow light at 555 nm. Light with the radiant intensity at other wavelengths has a lower luminous intensity. The curve which measures the response of the human eye to light is a defined standard, known as the luminosity function. Denoted V or y ¯, is based on an average of widely differing experimental data from scientists using different measurement techniques. For instance, the measured responses of the eye to light varied by a factor of ten. Luminous intensity should not be confused with another photometric unit, luminous flux, the total perceived power emitted in all directions. Luminous intensity is the perceived power per unit solid angle. If the optics were changed to concentrate the beam into 1/2 steradian then the source would have a luminous intensity of 2 candela. The resulting beam is brighter, though its luminous flux remains unchanged. Luminous intensity is also not the same as the corresponding objective physical quantity used in the measurement science of radiometry. The frequency of light used in the definition corresponds to a wavelength of 555 nm, near the peak of the eye's response to light. If the source emitted uniformly in all directions, the total flux would be about 18.40 mW, since there are 4π steradians in a sphere.
Luminous intensity
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Base quantity
272.
Candela
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A common candle emits light with a luminous intensity of roughly one candela. If emission in some directions is blocked by an opaque barrier, the emission would still be approximately one candela in the directions that are not obscured. The candela means candle in Latin. The definition describes how to produce a light source that emits one candela. Such a source could then be used to calibrate instruments designed to measure luminous intensity. The candela is sometimes still called by the modern definition of candlepower. The frequency chosen is in the visible spectrum near green, corresponding to a wavelength of about 555 nanometres. The human eye is most sensitive to this frequency, when adapted for bright conditions. At other frequencies, more radiant intensity is required to achieve the same intensity, according to the frequency response of the human eye. If more than one wavelength is present, one must integrate over the spectrum of wavelengths present to get the total luminous intensity. A common candle emits light with roughly 1 cd luminous intensity. Focused into a 20 ° beam, it will have an intensity of around 000 cd. The luminous intensity of light-emitting diodes is measured in thousandths of a candela. Indicator LEDs are typically in the 50 range; "ultra-bright" LEDs can reach 15 000 mcd, or higher. Prior to 1948, various standards for luminous intensity were in use in a number of countries.
Candela
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Photopic (black) and scotopic (green) luminosity functions. The photopic includes the CIE 1931 standard (solid), the Judd–Vos 1978 modified data (dashed), and the Sharpe, Stockman, Jagla & Jägle 2005 data (dotted). The horizontal axis is wavelength in nm.
273.
SI derived unit
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The International System of Units specifies a set of seven base units from which all other SI units of measurement are derived. Each of these other units can be expressed as a product of powers of one or more of the base units. For example, the SI derived unit of density is the kilogram per cubic metre. The degree Celsius is arguably an exception to this rule. The names of SI units are written in lowercase. The symbols for units named after persons, however, are always written with an initial letter. In addition to the two dimensionless derived units steradian, 20 other derived units have special names. Some other units such as litre, tonne, bar and electron volt are not SI units, but are widely used in conjunction with SI units. Until 1995, the units were grouped as derived units. Klaus Homann, Nikola Kallay, IUPAC. Quantities, Units and Symbols in Physical Chemistry. Blackwell Science Inc. p. 72. CS1 maint: Multiple names: authors list
SI derived unit
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Base units
274.
Dimension of a physical quantity
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Converting from one dimensional unit to another is often somewhat complex. The concept of physical dimension was introduced by Joseph Fourier in 1822. If they have different dimensions, they can not be directly compared in quantity. For example, it is meaningless to ask whether a kilogram is greater than, less than an hour. Any physically meaningful equation will have the same dimensions on a property known as "dimensional homogeneity". Checking this is a common application of dimensional analysis. Dimensional analysis is also routinely used as a check on the plausibility of derived computations. It is generally used to categorize types of dependence on other units. Many measurements in the physical sciences and engineering are expressed as a concrete number -- a numerical quantity and a corresponding dimensional unit. Compound relations with "per" are expressed with division, e.g. 60 mi/1 h. Other relations can involve multiplication, combinations thereof. For example, units for time are normally chosen as base units. Units for volume, however, can compound units. Sometimes the names of units obscure that they are derived units. One newton is 1 ⋅ m/s2.
Dimension of a physical quantity
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Base quantity
275.
History of the metric system
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Concepts similar to those behind the metric system had been discussed in the 16th and 17th centuries. The metric system was to be, in the words of philosopher and Condorcet, "for all people for all time". Reference copies for both units were placed in the custody of the French Academy of Sciences. Due to the unpopularity of the new metric system, France had reverted to units similar to those of their old system. In 1837 the metric system was re-adopted by France, also during the first half of the 19th century was adopted by the scientific community. Maxwell proposed three base units: length, time. This concept attempts to describe electromagnetic forces in terms of these units encountered difficulties. The mole was added as a seventh unit in 1971. The practical implementation of the metric system was the system implemented by French Revolutionaries towards the end of the 18th century. Its key features were that: It was decimal in nature. It derived its unit sizes from nature. Units that have different dimensions are related to each other in a rational manner. Prefixes are used to denote sub-multiples of its units. These features had already been explored and expounded by various scholars and academics prior to the French metric system being implemented. Simon Stevin is credited with introducing the decimal system into general use in Europe.
History of the metric system
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Frontispiece of the publication where John Wilkins proposed a metric system of units in which length, mass, volume and area would be related to each other
History of the metric system
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James Watt, British inventor and advocate of an international decimalized system of measure
History of the metric system
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A clock of the republican era showing both decimal and standard time
History of the metric system
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Repeating circle – the instrument used for triangulation when measuring the meridian
276.
System of measurement
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A system of measurement is a collection of units of measurement and rules relating them to each other. Systems of measurement have historically been important, defined for the purposes of science and commerce. Systems of measurement in modern use include the metric system, United States customary units. This has spread around the world, replacing most customary units of measure. In most systems, length, time are base quantities. Other quantities, such as speed, are derived from the base set: for example, speed is distance per unit time. Such arrangements were satisfactory in their own contexts. The preference for a more universal and consistent system gradually spread with the growth of science. Changing a system has substantial financial and cultural costs which must be offset against the advantages to be obtained from using a more rational system. However pressure built up, including from engineers for conversion to a more rational, also internationally consistent, basis of measurement. The unifying characteristic is that there was some definition based on some standard. Eventually strides gave way to "customary units" to met the needs of merchants and scientists. In other recent systems, a single basic unit is used for each base quantity. Often secondary units are derived by multiplying by powers of ten, i.e. by simply moving the decimal point. Thus the metric unit of length is the metre; a distance of 1.234 m is 1,234 millimetres, or 0.001234 kilometres.
System of measurement
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A baby bottle that measures in three measurement systems—imperial (UK), US customary, and metric.
277.
Outline of the metric system
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The metric system can be described as all of the following: System -- set of interdependent components forming an integrated whole. System of measurement – set of units which can be used to specify anything which can be measured. Historically, systems of measurement were initially regulated to support trade and internal commerce. Units were not necessarily well inter-related or self-consistent. When later analyzed and scientifically, some quantities were designated as fundamental units, meaning all other needed units of measure could be derived from them. Introduction to the metric system International system of units is the system of units, officially endorsed under the Metre Convention since 1960. 1861 - Concept of unit coherence introduced by Maxwell - the base units were the centimetre, gram and second. History of metrication – metrication is the process by which legacy, national-specific systems of measurement were replaced by the metric system. Centimetre–gram–second system of units was the principal variant of the metric system that evolved in stages until it was superseded by SI. Metric system was a little-used variant of the metric system that normalised the acceleration due to gravity. Metre -- tonne -- second system of units was a variant of the metric system used in Russian industry between the First and Second World Wars. In that year, seventeen nations signed the management and administration of the system passed into international control. Metre Convention describes its development to the modern day. Three organisations, the CGPM, BIPM were set up under the convention. General Conference on Weights and Measures – a meeting every four to six years of delegates from all member states.
Outline of the metric system
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"The metric system is for all people for all time." (Condorcet 1791) Four objects used in making measurements in everyday situations that have metric calibrations are shown: a tape measure calibrated in centimetres, a thermometer calibrated in degrees Celsius, a kilogram mass, and an electrical multimeter which measures volts, amps and ohms.
278.
SI units
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The International System of Units is the modern form of the metric system, is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units. The system was published in 1960 as the result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units rather than any variant of the centimetre-gram-second system. The International System of Units has been adopted by most developed countries; however, the adoption has not been universal in all English-speaking countries. The metric system was first implemented during the French Revolution with just the kilogram as standards of mass respectively. In the 1830s Carl Friedrich Gauss laid the foundations based on length, time. Meanwhile, in 1875, the Treaty of the Metre passed responsibility to international control. In 1921, the Treaty was extended to include all physical quantities including electrical units originally defined in 1893. The units associated with these quantities were the metre, kilogram, second, candela. In 1971, a seventh base quantity, amount of substance represented by the mole, was added to the definition of SI. On 11 the committee are, litre and grave for the units of length, area, capacity, mass, respectively. On 10 December 1799, the law by which the metric system was to be definitively adopted in France was passed. Prior to this, the strength of the earth’s magnetic field had only been described in relative terms. The resultant calculations enabled him to assign dimensions based on mass, length and time to the magnetic field.
SI units
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Stone marking the Austro-Hungarian /Italian border at Pontebba displaying myriametres, a unit of 10 km used in Central Europe in the 19th century (but since deprecated).
SI units
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The seven base units in the International System of Units
SI units
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Carl Friedrich Gauss
SI units
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Thomson
279.
Absement
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Absement changes as an object stays constant as the object resides at the initial position. It is the first time-integral of the displacement, so the displacement is the rate of change of the absement. The dimension of absement is length multiplied by time. Its SI unit is second, which corresponds to an object having been displaced by 1 meter for 1 second. This is not to be confused with a meter per second, the time-derivative of position. The amount of water having flown through it is linearly proportional to the absement of the gate, so it is also the same in both cases. The absement is a portmanteau of the words absence and displacement. Similarly, absition is a portmanteau of the words position. In this context, it gives rise to a new quantity called actergy, to energy as energy is to power. Actergy is the time-integral of total energy. Fluid flow in a throttle: A vehicle's distance travelled results from its throttle's absement. The longer it's been open, the more the vehicle's travelled. See "Analytic Displacement and Absement" versus "Piecewise Continuous Displacement and Absement". Velocity acceleration jerk position displacement Integral kinematics
Absement
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Ryan Janzen, playing with Hart House Symphonic Band
Absement
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Waterflute (reedless) hydraulophone with 45 finger-embouchure holes, allowing an intricate but polyphonic embouchure-like control by inserting one finger into each of several of the instrument's 45 mouths at once
Absement
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Aquatune Hydraulophone at the main entrance to the Legoland waterpark in Carlsbad California. This hydraulophone is in the shape of giant lego blocks.
Absement
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Hot tub hydraulophone
280.
Distance
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Distance is a numerical description of how far apart objects are. In everyday usage, distance may refer to a physical length, or an estimation based on other criteria. In most cases, "distance from A to B" is interchangeable with "distance from B to A". In mathematics, metric is a generalization of the concept of physical distance. In ω = 2πƒ is often used, where ƒ is the frequency. "distance", formalized as Chebyshev distance, is the minimum number of moves a king must make on a chessboard to travel between two squares. The term "distance" is also used by analogy to measure non-physical entities in certain ways. In science, there is the notion of the "edit distance" between two strings. For example, the words "dog" and "dot", which vary by only one letter, are closer than "dog" and "cat", which differ by three letters. Distance travelled never decreases. Distance is a magnitude, whereas displacement is a vector quantity with both magnitude and direction. Directed distance is a positive, negative scalar quantity. In general the straight-line distance does not equal distance travelled, for journeys in a straight line. Directed distances are distances with a directional sense. They can be determined along curved lines.
Distance
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d (A, B) > d (A, C) + d (C, B)
281.
Position (vector)
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Usually denoted x, r, or s, it corresponds to the straight-line distances along each axis from O to P: r = O P →. The term "vector" is used mostly in the fields of differential geometry, occasionally vector calculus. Frequently this is used in two-dimensional or three-dimensional space, but can be easily generalized to Euclidean spaces in any number of dimensions. Corresponding basis vectors represent the same vector. More general curvilinear coordinates are in contexts like general relativity. Linear algebra allows for the abstraction of an n-dimensional position vector. The notion of "space" is intuitive since each xi can be any value, the collection of values defines a point in space. The dimension of the position space is n. The coordinates of the vector r with respect to the basis vectors ei are xi. The vector of coordinates forms the coordinate vector or n-tuple. Each coordinate xi may be parameterized a number of parameters t. The linear span of a basis set B = equals the R, denoted span = R. In the case of one dimension, the position has only one component, so it effectively degenerates to a scalar coordinate. It could be, say, a vector in the x-direction, or the radial r-direction. These derivatives have common utility in the study of kinematics, other sciences.
Position (vector)
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Space curve in 3D. The position vector r is parameterized by a scalar t. At r = a the red line is the tangent to the curve, and the blue plane is normal to the curve.
282.
Area
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Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. It is the two-dimensional analog of the volume of a solid. The area of a shape can be measured by comparing the shape to squares of a fixed size. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the area of any other shape or surface is a dimensionless real number. There are well-known formulas for the areas of simple shapes such as triangles, rectangles, circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cylinder, the area of its boundary surface is called the surface area. Area plays an important role in modern mathematics. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. It can be proved that such a function exists.
Area
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A square metre quadrat made of PVC pipe.
Area
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The combined area of these three shapes is approximately 15.57 squares.
283.
Square metre
Square metre
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Comparison of 1 Square metre with some Imperial and metric units of area
284.
Radian
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The radian is the standard unit of angular measure, used in many areas of mathematics. This category was abolished in 1995 and the radian is now considered an SI derived unit. Separately, the SI unit of solid measurement is the steradian. The radian is represented by the rad. So for example, a value of 1.2 radians could be written as 1.2 rad, 1.2 r, 1.2rad, or 1.2c. Radian describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc. One radian is the angle subtended by an arc, equal in length to the radius of the circle. Conversely, the length of the enclosed arc is equal to the radius multiplied in radians;, s = rθ. When degrees are meant the symbol ° is used. Thus 2π radians is equal to 360 degrees, meaning that one radian is equal to 180/π degrees. The concept of measure, as opposed to the degree of an angle, is normally credited to Roger Cotes in 1714. He recognized its naturalness as a unit of angular measure. The idea of measuring angles by the length of the arc was already by other mathematicians. For example, they also used sexagesimal subunits of the diameter part. The radian first appeared in print on 5 June 1873, in examination questions set by James Thomson at Queen's College, Belfast.
Radian
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A chart to convert between degrees and radians
Radian
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An arc of a circle with the same length as the radius of that circle corresponds to an angle of 1 radian. A full circle corresponds to an angle of 2 π radians.
285.
Solid angle
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In geometry, a solid angle is the two-dimensional angle in three-dimensional space that an object subtends at a point. It is a measure of how large the object appears to an observer looking from that point. In the International System of Units, a solid angle is expressed in a dimensionless unit called a steradian. A small object nearby may subtend the solid angle as a larger object farther away. For example, although the Moon is much smaller than the Sun, it is also much closer to Earth. Indeed, as viewed from any point on Earth, both objects have approximately the solid angle as well as apparent size. This is evident during a solar eclipse. Solid angles are often used in particular astrophysics. The solid angle of an object, very away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. Solid angles can also be measured in square degrees, in fractions of the sphere, also known as spat. At the equator you see all of the celestial sphere, at either pole only one half. Define θb, θc correspondingly. Let φab define φac, φbc correspondingly. When implementing the above care must be taken with the atan function to avoid negative or incorrect solid angles.
Solid angle
–
Any area on a sphere which is equal in area to the square of its radius, when observed from its center, subtends precisely one steradian.
286.
Steradian
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The steradian or square radian is the SI unit of solid angle. It is used in three-dimensional geometry, is analogous to the radian which quantifies planar angles. The name is derived from the Latin radius for "beam". It is useful, however, to distinguish between dimensionless quantities of a different nature, so the symbol "sr" is used to indicate a solid angle. For example, radiant intensity can be measured in watts per steradian. The steradian is now considered an SI derived unit. A steradian can be defined as the solid angle subtended by a area on its surface. For a general sphere of radius r, any portion of its surface with area A = r2 subtends one steradian. Because the A of a sphere is 4πr2, the definition implies that a sphere measures 4π steradians. By the same argument, the maximum solid angle that can be subtended at any point is 4π sr. Since A = r2, it corresponds to the area of a spherical cap, the relationship h/r = 1/2π holds. This angle corresponds to the angle of 2θ ≈ 1.144 rad or 65.54 °. The solid angle of a cone whose the 2θ is: Ω = 2 π s r. So to give an example, a measurement of the width of an object seen would be given in radians. At the same time its visible area over one's visible field would be given in steradians.
Steradian
–
A graphical representation of 1 steradian. The sphere has radius r, and in this case the area A of the highlighted surface patch is r 2. The solid angle Ω equals A sr/ r 2 which is 1 sr in this example. The entire sphere has a solid angle of 4π sr.
287.
Hertz
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The hertz is the unit of frequency in the International System of Units and is defined as one cycle per second. It is named for the first person to provide conclusive proof of the existence of electromagnetic waves. Hertz are commonly expressed in SI multiples kilohertz, megahertz, terahertz. Some of the unit's most common uses are in musical tones, particularly those used in radio - and audio-related applications. It is also used to describe the speeds at which other electronics are driven. The hertz s − 1. In English, "hertz" is also used as the form. As an SI unit, Hz can be prefixed; commonly used multiples are kHz, MHz, GHz and THz. One hertz simply means "one cycle per second"; 100 Hz means "hundred cycles per second", so on. The rate of stochastic events occur is expressed in reciprocal second or inverse second in general or, the specific case of radioactive decay, becquerels. Whereas 1 Hz is 1 cycle per second, 1 Bq is 1 aperiodic event per second. This SI unit is named after Heinrich Hertz. As with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2. The hertz is named after the German physicist Heinrich Hertz, who made scientific contributions to the study of electromagnetism.
Hertz
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Details of a heartbeat as an example of a non- sinusoidal periodic phenomenon that can be described in terms of hertz. Two complete cycles are illustrated.
Hertz
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A sine wave with varying frequency
288.
Kinematic viscosity
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The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. For liquids, it corresponds to the informal concept of "thickness"; for example, honey has a much higher viscosity than water. For a given pattern, the stress required is proportional to the fluid's viscosity. A fluid that has no resistance to shear stress is known as an inviscid fluid. Zero viscosity is observed only at very low temperatures in superfluids. Otherwise, all fluids are technically said to be viscous or viscid. A fluid such as pitch, may appear to be a solid. The word "viscosity" is derived from the Latin "viscum", also a viscous glue made from mistletoe berries. The dynamic viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds. This fluid has to be homogeneous at different shear stresses. An external force is therefore required in order to keep the top plate moving at constant speed. The proportionality μ in this formula is the viscosity of the fluid. The y-axis, perpendicular to the flow, points in the direction of maximum shear velocity. This equation can be used where the velocity does not vary linearly with y, such as in fluid flowing through a pipe. Use of the Greek mu for the dynamic stress viscosity is common among mechanical and chemical engineers, as well as physicists.
Kinematic viscosity
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Pitch has a viscosity approximately 230 billion (2.3 × 10 11) times that of water.
Kinematic viscosity
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A simulation of substances with different viscosities. The substance above has lower viscosity than the substance below
Kinematic viscosity
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Example of the viscosity of milk and water. Liquids with higher viscosities make smaller splashes when poured at the same velocity.
Kinematic viscosity
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Honey being drizzled.
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Jerk (physics)
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There is no generally used term to describe its scalar magnitude. According to the result of dimensional analysis of jerk, the SI units are m/s3; jerk can also be expressed in standard gravity per second. . . , where a → is acceleration, v → is velocity, r → is position, t is time. J is commonly used. Newton's notation for the derivative is also applied. The fourth derivative of position, equivalent to the first derivative of jerk, is jounce. Because of involving third derivatives, in differential equations of the form J = 0 are called jerk equations. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are accordingly called hyperjerk systems. As an everyday example, driving in a car can show effects of jerk. Beginners provide a jerky ride. This is the force of the acceleration. Note that there would be no jerk if the car started to move backwards with the same acceleration.
Jerk (physics)
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Timing diagram over one rev. for angle, angular velocity, angular acceleration, and angular jerk
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Kilogram square metre
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It depends on the axis chosen, with larger moments requiring more torque to change the body's rotation. It is an extensive property: the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems. For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia to the plane. When a body is free to rotate, around an axis, a torque must be applied to change its angular momentum. The amount of torque needed for any given rate of change in momentum is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of metre squared in SI units and pound-square feet in imperial or US units. The moment of inertia depends on how mass will vary depending on the chosen axis. In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, known as a compound pendulum. There is an interesting difference in the moment of inertia appears in planar and spatial movement. The moment of inertia of a rotating flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. If the momentum of a system is constant, then as the moment of inertia gets smaller, the angular velocity must increase. This occurs when spinning figure skaters pull in their outstretched divers curl their bodies into a tuck position during a dive, to spin faster. Moment of inertia can be measured using a simple pendulum, because it is the resistance to the rotation caused by gravity. Here r is the distance perpendicular to and from the force to the torque axis. Here F is the tangential component of the net force on the mass.
Kilogram square metre
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Tightrope walker Samuel Dixon using the long rod's moment of inertia for balance while crossing the Niagara River in 1890.
Kilogram square metre
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Flywheels have large moments of inertia to smooth out mechanical motion. This example is in a Russian museum.
Kilogram square metre
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Spinning figure skaters can reduce their moment of inertia by pulling in their arms, allowing them to spin faster due to conservation of angular momentum.
Kilogram square metre
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Pendulums used in Mendenhall gravimeter apparatus, from 1897 scientific journal. The portable gravimeter developed in 1890 by Thomas C. Mendenhall provided the most accurate relative measurements of the local gravitational field of the Earth.
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List of equations in classical mechanics
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Classical mechanics is the branch of physics used to describe the motion of macroscopic objects. It is the most familiar of the theories of physics. The concepts it covers, such as mass, force, are commonly used and known. The subject is based upon a three-dimensional Euclidean space with fixed axes, called a frame of reference. The point of concurrency of the three axes is known as the origin of the particular space. Classical mechanics utilises many equations -- well as other mathematical concepts -- which relate various physical quantities to one another. These include differential equations, manifolds, ergodic theory. This page gives a summary of the most important of these. This article lists equations from Newtonian mechanics, see analytical mechanics for the more general formulation of classical mechanics. Every conservative force has a potential energy. Whenever the force does work, potential energy is lost. In the rotational definitions, the angle can be any angle about the specified axis of rotation. This does not have to be the polar angle used in polar coordinate systems. The precession speed of a spinning top is given by: Ω = w r I ω where w is the weight of the spinning flywheel. Euler also worked out analogous laws of motion to those of Newton, see Euler's laws of motion.
List of equations in classical mechanics
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Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
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Newton (unit)
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The newton is the International System of Units derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion. See below for the conversion factors and SI unitizing. In 1948, the 9th CGPM resolution 7 adopted the name "newton" for this force. The MKS system then became the blueprint for today's SI system of units. The newton thus became the standard unit of force in le Système International d'Unités, or International System of Units. This SI unit is named after Isaac Newton. As with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2. The newton is therefore: where the following symbols are used for the units: kg for kilogram, s for second. In dimensional analysis: F = M L T 2 where F is force, M is mass, L is length and T is time. At average gravity on earth, a kilogram mass exerts a force of about 9.8 newtons. An average-sized apple exerts about one newton of force, which we measure as the apple's weight. 441 N = 45 kg × 9.80665 m/s2 It is common to see forces expressed in kilonewtons where 1 kN = 1000 N. For example, the tractive effort of a Class Y steam train and the thrust of an F100 fighter jet are both around 130 kN.
Newton (unit)
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Base units
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Joule
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The joule, symbol J, is a derived unit of energy in the International System of Units. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule. This relationship can be used to define the volt. The work required to produce one "watt second". This relationship can be used to define the watt. This SI unit is named after James Prescott Joule. As with every International System of Units unit named for a person, the first letter of its symbol is upper case. Note that "degree Celsius" conforms to this rule because the "d" is lowercase.— Based on The International System of Units, section 5.2. But they are not interchangeable. The use of joules for energy is helpful to avoid misunderstandings and miscommunications. The distinction may be seen also in the fact that energy is a scalar -- the product of a vector force and a vector displacement. By contrast, torque is a vector -- the cross product of a force vector. Since radians are dimensionless, it follows that energy have the same dimensions. One joule in everyday life represents approximately: The energy required to lift a medium-size tomato 1 meter vertically from the surface of the Earth.
Joule
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Base units
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Newton metre
Newton metre
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Conversion factors [edit]
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Integrated Authority File
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The Integrated Authority File or GND is an international authority file for the organisation of personal names, subject headings and corporate bodies from catalogues. It is used mainly increasingly also by archives and museums. The GND is managed with various regional library networks in German-speaking Europe and other partners. The GND falls under the Creative Commons Zero license. The GND specification provides a hierarchy of high-level sub-classes, useful in library classification, an approach to unambiguous identification of single elements. It also comprises an ontology intended for knowledge representation in the semantic web, available in the RDF format.
Integrated Authority File
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GND screenshot
296.
National Diet Library
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The National Diet Library is the only national library in Japan. It was established for the purpose of assisting members of the National Diet of Japan in researching matters of public policy. The library is similar in scope to the United States Library of Congress. The National Diet Library consists of several other branch libraries throughout Japan. Its need for information was "correspondingly small." The original Diet libraries "never developed either the services which might have made them vital adjuncts of genuinely responsible legislative activity." Until Japan's defeat, moreover, the executive had controlled all political documents, depriving the Diet of access to vital information. In 1946, each house of the Diet formed its own National Diet Library Standing Committee. Hani envisioned the new body as "both a ` citadel of popular sovereignty," and the means of realizing a "peaceful revolution." The National Diet Library opened with an initial collection of 100,000 volumes. The first Librarian of the Diet Library was the politician Tokujirō Kanamori. The philosopher Masakazu Nakai served as the first Vice Librarian. In 1949, the NDL became the only national library in Japan. At this time the collection gained an additional million volumes previously housed in the former National Library in Ueno. In 1961, the NDL opened at its present location in Nagatachō, adjacent to the National Diet.
National Diet Library
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Tokyo Main Library of the National Diet Library
National Diet Library
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Kansai-kan of the National Diet Library
National Diet Library
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The National Diet Library
National Diet Library
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Main building in Tokyo
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Mass
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In physics, mass is a property of a physical body. It is the measure of an object's resistance to acceleration when a force is applied. It also determines the strength of its gravitational attraction to other bodies. In the theory of relativity a related concept is the mass -- content of a system. The SI unit of mass is the kilogram. It would still have the same mass. This is because weight is a force, while mass is the property that determines the strength of this force. In Newtonian physics, mass can be generalized in an object. However, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, all forms of energy resist acceleration by a force and have gravitational attraction. In addition, "matter" thus can not be precisely measured. There are distinct phenomena which can be used to measure mass. Gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the gravitational force exerted on an object in a gravitational field. Mass–energy measures the total amount of energy contained within a body, using E = mc2.
Mass
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Depiction of early balance scales in the Papyrus of Hunefer (dated to the 19th dynasty, ca. 1285 BC). The scene shows Anubis weighing the heart of Hunefer.
Mass
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The kilogram is one of the seven SI base units and one of three which is defined ad hoc (i.e. without reference to another base unit).
Mass
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Galileo Galilei (1636)
Mass
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Distance traveled by a freely falling ball is proportional to the square of the elapsed time