1.
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)
2.
SI unit
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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 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
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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 unit
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The seven base units in the International System of Units
SI unit
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Carl Friedrich Gauss
SI unit
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Thomson
3.
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.
4.
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
5.
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
6.
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
7.
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.
8.
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
9.
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
10.
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.
11.
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
12.
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.
13.
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
14.
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.
15.
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
16.
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.
17.
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.
18.
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)
19.
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
20.
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.
21.
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
22.
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
23.
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.
24.
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
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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.
25.
Space
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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
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Gottfried Leibniz
Space
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A right-handed three-dimensional Cartesian coordinate system used to indicate positions in space.
Space
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Isaac Newton
Space
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Immanuel Kant
26.
Time
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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
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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
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Horizontal sundial in Taganrog
Time
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A contemporary quartz watch
27.
Torque
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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
28.
Velocity
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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
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As a change of direction occurs while the cars turn on the curved track, their velocity is not constant.
29.
Virtual work
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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
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This is an engraving from Mechanics Magazine published in London in 1824.
Virtual work
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Illustration from Army Service Corps Training on Mechanical Transport, (1911), Fig. 112 Transmission of motion and force by gear wheels, compound train
30.
Newton's laws 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 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
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Newton's First and Second laws, in Latin, from the original 1687 Principia Mathematica.
Newton's laws of motion
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Isaac Newton (1643–1727), the physicist who formulated the laws
31.
Analytical mechanics
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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
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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).
32.
Lagrangian mechanics
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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
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Isaac Newton (1642—1726)
Lagrangian mechanics
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Jean d'Alembert (1717—1783)
33.
Routhian mechanics
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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.
34.
Damping
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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
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Mass attached to a spring and damper.
35.
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
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The effect of varying damping ratio on a second-order system.
36.
Displacement (vector)
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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)
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Displacement versus distance traveled along a path
37.
Equations of motion
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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
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Kinematic quantities of a classical particle of mass m: position r, velocity v, acceleration a.
38.
Fictitious force
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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
39.
Friction
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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
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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.
40.
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
41.
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.
42.
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
43.
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.
44.
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
45.
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.
46.
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
–
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).
47.
Rigid body dynamics
–
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
–
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
48.
Vibration
–
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).
49.
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
–
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
50.
Centripetal force
–
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
–
A body experiencing uniform circular motion requires a centripetal force, towards the axis as shown, to maintain its circular path.
51.
Centrifugal force
–
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
–
The interface of two immiscible liquids rotating around a vertical axis is an upward-opening circular paraboloid.
52.
Reactive centrifugal force
–
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
–
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.
53.
Coriolis force
–
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
–
This low-pressure system over Iceland spins counter-clockwise due to balance between the Coriolis force and the pressure gradient force.
Coriolis force
–
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
–
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.
54.
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)
–
Figure 1. Force diagram of a simple gravity pendulum.
Pendulum (mathematics)
–
Animation of a pendulum showing the velocity and acceleration vectors.
55.
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.
56.
Angular displacement
–
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
–
Rotation of a rigid object P about a fixed object about a fixed axis O.
57.
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
–
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.
58.
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
59.
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
–
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
60.
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)
61.
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
62.
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
63.
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
–
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
64.
Jean le Rond d'Alembert
–
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
65.
Alexis Clairaut
–
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
66.
Joseph-Louis Lagrange
–
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
–
Lagrange's tomb in the crypt of the Panthéon
67.
Pierre-Simon Laplace
–
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
–
Pierre-Simon Laplace (1749–1827). Posthumous portrait by Jean-Baptiste Paulin Guérin, 1838.
Pierre-Simon Laplace
–
Laplace's house at Arcueil.
Pierre-Simon Laplace
–
Laplace.
Pierre-Simon Laplace
–
Tomb of Pierre-Simon Laplace
68.
William Rowan Hamilton
–
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
–
Quaternion Plaque on Broom Bridge
William Rowan Hamilton
–
William Rowan Hamilton (1805–1865)
William Rowan Hamilton
–
Irish commemorative coin celebrating the 200th Anniversary of his birth.
69.
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
70.
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
–
Johann Bernoulli (portrait by Johann Rudolf Huber, circa 1740)
71.
Augustin-Louis Cauchy
–
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
–
Cauchy around 1840. Lithography by Zéphirin Belliard after a painting by Jean Roller.
Augustin-Louis Cauchy
–
The title page of a textbook by Cauchy.
Augustin-Louis Cauchy
–
Leçons sur le calcul différentiel, 1829
72.
Time derivative
–
A time derivative is a derivative of a function with respect to time, usually interpreted as the rate of change of the value of the function. The variable time is usually written as t. A variety of notations are used to denote the derivative. In addition to the normal notation, d x d t A very common short-hand notation used, especially in physics, is the'over-dot'. I.E. That is, d V → d t =. Time derivatives are a key concept in physics. Even higher derivatives are sometimes also used: the third derivative of position with respect to time is known as the jerk. See motion derivatives. A large number of fundamental equations in physics involve second time derivatives of quantities. A common occurrence in physics is the time derivative such as velocity or displacement. In dealing with such a derivative, both orientation may depend upon time. For example, consider a particle moving in a circular path. With this form for the displacement, the velocity now is found. The derivative of the displacement vector is the velocity vector.
Time derivative
–
Relation between Cartesian coordinates (x, y) and polar coordinates (r, θ).
73.
Position (vector)
–
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)
–
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.
74.
Time in physics
–
Time in physics is defined by its measurement: time is what a clock reads. In non-relativistic physics it is a scalar quantity and, like length, mass, charge, is usually described as a fundamental quantity. Time can be combined mathematically with physical quantities to derive other concepts such as motion, kinetic energy and time-dependent fields. Timekeeping is part of the foundation of recordkeeping. Simultaneously, our conception of time has evolved, as shown below. In the International System of Units, the unit of time is the second. This definition is based on the operation of a atomic clock. The UTC timestamp in use worldwide is an atomic standard. The relative accuracy of such a standard is currently on the order of 10 − 15. Most people up until the 20th century thought that time was the same for everyone everywhere. This is the basis for timelines, where time is a parameter. Thus time is part of a coordinate, in this view. Therefore time itself began about 13.8 billion years ago in the big bang; see time in Cosmology below. Whether it will ever come to an end is an open question. In order to measure time, one can record the number of occurrences of some periodic phenomenon.
Time in physics
–
Foucault 's pendulum in the Panthéon of Paris can measure time as well as demonstrate the rotation of Earth.
Time in physics
–
Andromeda galaxy (M31) is two million light-years away. Thus we are viewing M31's light from two million years ago, a time before humans existed on Earth.
Time in physics
–
WMAP fluctuations of the cosmic microwave background radiation.
Time in physics
–
Key concepts
75.
Limit (mathematics)
–
In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are used to define continuity, derivatives, integrals. C is a real number. In that case, the above equation can be read as "the limit of f of x, as x approaches c, is L". Augustin-Louis Cauchy in 1821, followed by Karl Weierstrass, formalized the definition of the limit of a function which became known as the -definition of limit. Note that the above definition of a limit is true even if f ≠ L. Indeed, the f need not even be defined at c. In addition to limits at finite values, functions can also have limits at infinity. In this case, the limit of f as x approaches infinity is 2. In mathematical notation, lim x → ∞ 2 x − x = 2. Consider the following sequence: 1.79, 1.799, 1.7999... It can be observed that the numbers are "approaching" 1.8, the limit of the sequence. Formally, a2... is a sequence of real numbers. Not every sequence has a limit; if it does not, it is divergent. One can show that a sequence has only one limit. The limit of the limit of a function are closely related.
Limit (mathematics)
–
Whenever a point x is within δ units of c, f (x) is within ε units of L.
76.
Dimensional analysis
–
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 are incommensurable and cannot be directly compared in quantity. For example, it is meaningless to ask whether a kilogram is greater than, equal to, or less than an hour. Any physically meaningful equation will have the same dimensions on the left and right sides, 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 equations and computations. It is generally used to categorize types of physical quantities and units based on their relationship to or dependence on other units. Many measurements in the physical sciences and engineering are expressed as a concrete number -- a corresponding dimensional unit. Compound relations with "per" are expressed with division, e.g. 60 mi/1 h. Other relations can involve combinations thereof. For example, units for length and time are normally chosen as base units. Units for volume, however, can be factored into the base units of length, thus being derived or compound units. Sometimes the names of units obscure that they are derived units. One newton is 1 kg⋅m/s2.
Dimensional analysis
–
Base quantity
77.
International System of Units
–
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
–
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
–
The seven base units in the International System of Units
International System of Units
–
Carl Friedrich Gauss
International System of Units
–
Thomson
78.
Kilometre per hour
–
The kilometre per hour is a unit of speed, expressing the number of kilometres travelled in one hour. The unit symbol is km/h Worldwide, it is the most commonly used unit of speed on road signs and car speedometers. The Dutch on the other hand adopted the kilometre in 1817 but gave it the local name of the mijl. The SI representations, classified as symbols, are "km/h", "km h−1" and "km·h−1". Abbreviations for "kilometres per hour" did not appear until the late century. "Kilometres per hour" did not begin to be abbreviated in print until many years later, with several different abbreviations existing near-contemporaneously. For example, news organisations such as Reuters and The Economist require "kph". In unofficial usage, km/h is sometimes written as clicks. In the early 1800s Berzelius introduced a symbolic notation for the chemical elements derived from the elements' Latin names. Typically, "Na" was used for the element sodium and H2O for water. Among these were the use of the symbol "km" for "kilometre". The SI explicitly states that unit symbols are not abbreviations and are to be written using a very specific set of rules. Hence the name of the unit can be replaced by a kind of algebraic symbol, shorter and easier to use in formulae. This symbol is merely a symbol which, like chemical symbols, must be used in a prescribed manner. SI, hence the use of "km/h" has now been adopted around the world in many areas related to health and safety and in metrology.
Kilometre per hour
–
A car speedometer that indicates measured speed in kilometres per hour.
Kilometre per hour
–
Automobile speedometer, measuring speed in miles per hour on the outer track, and kilometres per hour on the inner track. In Canada "km/h" is shown on the outer track and "MPH" on the inner track.
79.
Miles per hour
–
Miles per hour is an imperial and United States customary unit of speed expressing the number of statute miles covered in one hour. Miles per hour is the unit also used in the Canadian system, which uses km/h on roads. In some countries mph may be used to express the speed of delivery of a ball in sporting events such as cricket, baseball. Road traffic speeds in other countries are indicated in kilometres per hour, while occasionally both systems are used. In Ireland, a judge considered a speeding case by examining speeds in both kilometres per hour and miles per hour. Aeronautical applications, however, favour the knot as a common unit of speed. 1 Mph = 0.000277778 Mps Example: Apollo 11 attained speeds of 25,000 Mph, which converts to about 7 Mps. If Apollo 11 were to travel to Los Angeles it would reach Los Angeles in under 6 minutes.
Miles per hour
–
Automobile speedometer, indicating speed in miles per hour on the outer scale and kilometres per hour on the inner scale
Miles per hour
–
United States road sign with maximum speed noted in standard Mph
80.
Knot (unit)
–
The knot is a unit of speed equal to one nautical mile per hour, approximately 1.151 mph. The ISO Standard symbol for the knot is kn. The same symbol is preferred by the IEEE; kt is also common. The knot is a non-SI unit, "accepted for use with the SI". Etymologically, the term derives from counting the number of knots in the line that unspooled from the reel of a chip log in a specific time. 1 international knot = 1 nautical mile per hour, 1.852 kilometres per hour, 20.254 inches per second. 7003185200000000000♠1852 m is the length of the internationally agreed nautical mile. The US adopted the international definition in 1954, having previously used the US nautical mile. The UK adopted the nautical definition in 1970, having previously used the UK Admiralty nautical mile. The speeds of vessels relative to the fluids in which they travel are measured in knots. For consistency, the speeds of navigational fluids are also measured in knots. Thus, speed over the ground and rate of progress towards a distant point are also given in knots. Until the mid-19th century, speed at sea was measured using a log. The log was "cast" over the stern of the line allowed to pay out. The count would be used in the sailing master's dead reckoning and navigation.
Knot (unit)
–
Graphic scale from a Mercator projection world map, showing the change with latitude
81.
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.
82.
Speed of light
–
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
–
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
–
Sunlight takes about 8 minutes 17 seconds to travel the average distance from the surface of the Sun to the Earth.
Speed of light
–
Diagram of the Fizeau apparatus
Speed of light
–
Rømer's observations of the occultations of Io from Earth
83.
Matter
–
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
–
Matter
Matter
Matter
Matter
84.
Derivative
–
The derivative of a function of a real variable measures the sensitivity to change of a quantity, determined by another quantity. Derivatives are a fundamental tool of calculus. The line is the best linear approximation of the function near that input value. Derivatives may be generalized to functions of real variables. In this generalization, the derivative is reinterpreted as a linear transformation whose graph is the best linear approximation to the graph of the original function. The Jacobian matrix is the matrix that represents this linear transformation with respect to the basis given by the choice of dependent variables. It can be calculated to the independent variables. For a real-valued function of several variables, the Jacobian matrix reduces to the gradient vector. The process of finding a derivative is called differentiation. The reverse process is called antidifferentiation. The fundamental theorem of calculus states that antidifferentiation is the same as integration. Integration constitute the two fundamental operations in single-variable calculus. Differentiation is the action of computing a derivative. It is called the derivative of f with respect to x. Thus, since y + Δ y = y + m Δ x, it follows that Δ y = m Δ x.
Derivative
–
The graph of a function, drawn in black, and a tangent line to that function, drawn in red. The slope of the tangent line is equal to the derivative of the function at the marked point.
85.
Speedometer
–
A speedometer or a speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. Now universally fitted to motor vehicles, they started to be available as standard equipment from about 1910 onwards. Speedometers for other vehicles use other means of sensing speed. For a boat, this is a log. For an aircraft, this is an airspeed indicator. Charles Babbage is credited with creating an early type of a speedometer, which were usually fitted to locomotives. The electric speedometer was originally called a velocimeter. Many motorcycles, however, use a cable driven from a front wheel. When the motorcycle is in motion, a speedometer gear assembly turns a speedometer cable, which then turns the speedometer mechanism itself. As the magnet rotates near the cup, the changing magnetic field produces eddy currents in the cup, which themselves produce another magnetic field. The shaft is held toward zero by a fine torsion spring. The torque on the cup increases with the speed of rotation of the magnet. Thus an increase in the speed of the car will twist the cup and pointer against the spring. At a given speed the pointer will remain motionless and pointing to the appropriate number on the speedometer's dial. The spring is calibrated such that a given revolution speed of the cable corresponds to a specific speed indication on the speedometer.
Speedometer
–
A speedometer showing mph and km/h along with an odometer and a separate "trip" odometer (both showing distance traveled in miles).
86.
Slope
–
In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line. The direction of a line is either increasing, decreasing, vertical. A line is increasing if it goes up from left to right. The slope is positive, i.e. m 0. A line is decreasing if it goes down from left to right. The slope is negative, i.e. m 0. If a line is horizontal the slope is zero. This is a constant function. If a line is vertical the slope is undefined. The steepness, grade of a line is measured by the absolute value of the slope. Sometimes the ratio is expressed as a quotient, giving the same number for every two distinct points on the same line. A line, decreasing has a negative "rise". In mathematical language, the m of the line is m = y 2 − y 1 x 2 − x 1. The concept of slope applies directly to gradients in geography and civil engineering. Thereby, the simple idea of slope becomes one of the main basis of the modern world in terms of the built environment.
Slope
–
Slope illustrated for y = (3/2) x − 1. Click on to enlarge
Slope
–
Slope:
Slope
–
A 1371-meter distance of a railroad with a 20 ‰ slope. Czech Republic
Slope
–
Steam-age railway gradient post indicating a slope in both directions at Meols railway station, United Kingdom
87.
Tangent line
–
In geometry, the tangent line to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it through a pair of infinitely close points on the curve. A similar definition applies in n-dimensional Euclidean space. Similarly, the tangent plane to a surface at a given point is the plane that the surface at that point. The concept of a tangent has been extensively generalized; see Tangent space. The word "tangent" comes from the Latin tangere,'to touch'. Euclid makes several references to the tangent to a circle in book III of the Elements. In Apollonius work Conics he defines a tangent as being a line such that no straight line could fall between it and the curve. Archimedes found the tangent by considering the path of a point moving along the curve. Independently Descartes used his method of normals based on the observation that the radius of a circle is always normal to the circle itself. These methods led in the 17th century. René-François de Sluse and Johannes Hudde found algebraic algorithms for finding tangents. Further developments included those of Isaac Barrow, leading to the theory of Isaac Newton and Gottfried Leibniz. An 1828 definition of a tangent was "a right line which when produced, does not cut it". This old definition prevents inflection points from having any tangent.
Tangent line
–
Tangent to a curve. The red line is tangential to the curve at the point marked by a red dot.
88.
Chord (geometry)
–
A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite extension of a chord. More generally, a chord is a segment joining two points on any curve, for instance an ellipse. A chord that passes through a circle's point is the circle's diameter. The chord is from the Latin chorda meaning bowstring. Among properties of chords of a circle are the following: Chords are equidistant from the center if and only if their lengths are equal. A chord that passes through the center of a circle is the longest chord. If the line extensions of chords AB and CD intersect at a P, then their lengths satisfy AP · PB = CP · PD. The area that a circular chord "cuts off" is called a circular segment. The midpoints of a set of parallel chords of an ellipse are collinear. Chords were used extensively in the early development of trigonometry. The first trigonometric table, compiled by Hipparchus, tabulated the value of the chord function for every 7.5 degrees. The chord lengths are accurate to two base-60 digits after the integer part. The function is defined geometrically as shown in the picture. The chord of an angle is the length of the chord between two points on a circle separated by that angle.
Chord (geometry)
–
The red segment BX is a chord (as is the diameter segment AB).
89.
Merry-go-round
–
A carousel, roundabout, or merry-go-round, is an amusement ride consisting of a rotating circular platform with seats for riders. This leads to one of the galloper. Popular names are jumper, horseabout and flying horses. Sometimes, bench like seats are used and occasionally mounts can be shaped like aeroplanes or cars. The modern carousel emerged from early jousting traditions in the Middle East. Knights would gallop in a circle while tossing balls to another; an activity that required great skill and horsemanship. This game was introduced to Europe from earlier Byzantine and Arab traditions. The carousel originated from the Italian garosello and Spanish carosella. Cavalry spectacles that replaced medieval jousting, such as the ring-tilt, were popular in Italy and France. Carousels soon sprung up at fairgrounds across Europe. At the Place du Carrousel in Paris, an early make believe carousel was set up with wooden horses for the children. By the 18th century carousels were being built and operated at various fairs and gatherings in central Europe and England. Makers included Heyn in France. These early carousels had no platforms; the animals would fly out from the centrifugal force of the spinning mechanism. They were often powered by animals walking in people pulling a rope or cranking.
Merry-go-round
–
French old-fashioned style carousel with stairs in La Rochelle.
Merry-go-round
–
Australian racegoers enjoy a merry-go-round at the Deepwater Races, c. 1910.
Merry-go-round
–
Savage's amusement ride, Sea-On-Land, where the riders would pitch up and down as if they were on the sea.
Merry-go-round
–
Carousel built in 1905 by Gustav Dentzel which is still operational in Rochester, New York.
90.
Turntable
–
The phonograph is a device invented in 1877 for the mechanical recording and reproduction of sound. In its later forms it is also called a gramophone. The phonograph was invented by Thomas Edison. While other inventors had produced devices that could record sounds, Edison's phonograph was the first to be able to reproduce the recorded sound. His phonograph originally recorded sound onto a tinfoil sheet wrapped around a rotating cylinder. A stylus responding to sound vibrations produced an down or hill-and-dale groove in the foil. In the 1890s, Emile Berliner initiated the transition from phonograph cylinders with a spiral groove running from the periphery to near the center. Later improvements through the years included modifications to the turntable and its drive system, the sound and equalization systems. The disc record was the dominant audio recording format throughout most of the 20th century. Records are still a favorite format for DJs. Vinyl records are still used in their concert performances. Musicians continue to release their recordings on vinyl records. The original recordings of musicians are sometimes re-issued on vinyl. Usage of terminology is not uniform across the English-speaking world. In more modern usage, the device is often called a "turntable", "record player", or "record changer".
Turntable
–
Edison cylinder phonograph, circa 1899
Turntable
–
Thomas Edison with his second phonograph, photographed by Mathew Brady in Washington, April 1878
Turntable
–
Close up of the mechanism of an Edison Amberola, manufactured circa 1915
Turntable
–
A late 20th-century turntable and record
91.
Tangent lines to circles
–
In Euclidean plane geometry, a tangent line to a circle is a line that touches the circle at exactly one point, never entering the circle's interior. Roughly speaking, it is a line on the circle. Tangent lines to circles play an important role in many geometrical constructions and proofs. A tangent line t to a circle C intersects the circle at a single point T. For comparison, secant lines intersect a circle at two points, whereas another line may not intersect a circle at all. This property of tangent lines is preserved under geometrical transformations, such as scalings, rotation, translations, inversions, map projections. In technical language, these transformations do not change the structure of the tangent line and circle, even though the line and circle may be deformed. The radius of a circle is perpendicular to the tangent line through its endpoint on the circle's circumference. Conversely, the perpendicular to a radius through the same endpoint is a tangent line. The resulting geometrical figure of circle and line has a reflection symmetry about the axis of the radius. No line can be drawn through a point within a circle, since any such line must be a secant line. However, two tangent lines can be drawn from a point P outside of the circle. Thus the lengths of the segments from P to the two tangent points are equal. By the secant-tangent theorem, the square of this tangent length equals the power of the P in the circle C. This power equals the product of distances from P to any two intersection points of the circle with a secant line passing through P.
Tangent lines to circles
–
By the power-of-a-point theorem, the product of lengths PM·PN for any ray PMN equals to the square of PT, the length of the tangent line segment (red).
92.
Circumference
–
The circumference of a closed curve or circular object is the linear distance around its edge. The circumference of a circle is of special importance in geometry and trigonometry. Informally "circumference" may also refer to the edge itself rather than to the length of the edge. The circumference of a circle is the distance around it. The term is used when measuring physical objects, well as when considering geometric forms. The circumference of a circle relates to one of the most important mathematical constants in all of mathematics. Pi, is represented by the Greek π. The numerical value of π is 3.14159 26535 89793.... The above formula can be rearranged to solve for the circumference: C = π ⋅ d = 2 r. The use of the constant π is ubiquitous in mathematics, science. The constant ratio of circumference to radius C r = 2 π also has many uses in mathematics, science. These uses are not limited to radians, physical constants. The Greek τ is not generally accepted as proper notation. The circumference of an ellipse can be expressed in terms of the complete elliptic integral of the second kind. In graph theory the circumference of a graph refers to the longest cycle contained in that graph.
Circumference
–
Circle illustration with circumference (C) in black, diameter (D) in cyan, radius (R) in red, and centre or origin (O) in magenta. Circumference = π × diameter = 2 × π × radius.
93.
Omega
–
Omega is the 24th and last letter of the Greek alphabet. In the numeric system, it has a value of 800. The word literally means "great O", as opposed to omicron, which means "little O". In phonetic terms, the Greek Ω is a long open-mid o, comparable to the vowel of British English raw. In Modern Greek, Ω represents the same sound as omicron. The letter omega is transcribed ō or simply o. Omega is also used in Christianity, as a part of the Alpha and Omega metaphor. Ω was not part of the Greek alphabets. It was introduced in the 7th century BC in the Ionian cities of Asia Minor to denote the long half-open. It is a variant of omicron, broken up with the edges subsequently turned outward. The Ωμέγα is Byzantine; in Classical Greek, the letter was called ō, whereas the omicron was called ou. In addition to the Greek alphabet, Omega was also adopted into the Cyrillic alphabet. See Cyrillic omega. A Raetic variant is conjectured to be at the origin or evolution of the Elder Futhark ᛟ. Omega was also adopted into the Latin alphabet, to the African reference alphabet.
Omega
–
Greek alphabet
94.
Conversion of units
–
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.
Conversion of units
–
Base units
95.
SI derived unit
–
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
–
Base units
96.
Kilometres per hour
–
The kilometre per hour is a unit of speed, expressing the number of kilometres travelled in one hour. The unit symbol is km/h Worldwide, it is the most commonly used unit of speed on road signs and car speedometers. The Dutch on the other hand gave the local name of the mijl. The SI representations, classified as symbols, are "km/h", "km h−1" and "km·h−1". Abbreviations for "kilometres per hour" did not appear until the late nineteenth century. "Kilometres per hour" did not begin to be abbreviated in print until many years later, with several different abbreviations existing near-contemporaneously. For example, news organisations such as Reuters and The Economist require "kph". In unofficial usage, km/h is sometimes written as klicks or clicks. In the early 1800s Berzelius introduced a symbolic notation for the chemical elements derived from the elements' Latin names. Typically, "Na" was used for the H2O for water. Among these were the use of the symbol "km" for "kilometre". The SI explicitly states that unit symbols are not abbreviations and are to be written using a very specific set of rules. Hence the name of the unit can be replaced by a kind of algebraic symbol, shorter and easier to use in formulae. This symbol is merely a symbol which, like chemical symbols, must be used in a precise and prescribed manner. SI, hence the use of "km/h" has now been adopted around the world in many areas related to health and safety and in metrology.
Kilometres per hour
–
A car speedometer that indicates measured speed in kilometres per hour.
Kilometres per hour
–
Automobile speedometer, measuring speed in miles per hour on the outer track, and kilometres per hour on the inner track. In Canada "km/h" is shown on the outer track and "MPH" on the inner track.
97.
Nautical mile
–
A nautical mile is a unit of measurement defined as exactly 1852 meters. Historically, it was defined as one sixtieth of the distance between two parallels of latitude separated by one degree. The derived unit of speed is the knot, defined as one nautical mile per hour. The geographical mile is the length of one minute of longitude along about 1,855.325 m on the WGS 84 ellipsoid. There is no internationally agreed symbol. Nm is used by the U.S. National Oceanic and Atmospheric Administration. Nmi is used by the Institute of the United States Government Publishing Office. The mile is from the Latin word for a thousand paces: mīlia. In 1617 the Dutch Snell assessed the circumference of the Earth at 24,630 Roman miles. Around that time British mathematician Edmund Gunter improved navigational tools including a new quadrant to determine latitude at sea. As one degree is 1/360 of a circle, one minute of arc is 1/21600 of a circle. These sexagesimal units originated in Babylonian astronomy. Gunter used Snell's circumference to define a nautical mile at 48 degrees latitude. Other countries measure the minute of arc at 45 degrees latitude, giving the nautical mile a length of 6076 ft. In 1929, the international nautical mile was defined by the First International Extraordinary Hydrographic Conference in Monaco as 1,852 meters.
Nautical mile
–
Historical definition – 1 nautical mile
98.
Mach number
–
In fluid dynamics, the Mach number is a dimensionless quantity representing the ratio of flow velocity past a boundary to the local speed of sound. In the simplest explanation, the speed of Mach 1 is equal to the speed of sound. Therefore, Mach 1.35 is about 35 % faster than the speed of sound. Thereby the Mach number, depends on the condition of the surrounding medium, in particular the temperature and pressure. The Mach number is primarily used to determine the approximation with which a flow can be treated as an incompressible flow. The medium can be a liquid. As the Mach number is defined as the ratio of two speeds, it is a dimensionless number. A simplified incompressible flow equations can be used. The Mach number is named after philosopher Ernst Mach, a designation proposed by aeronautical engineer Jakob Ackeret. This is somewhat reminiscent of the modern ocean sounding unit "mark", also unit-first, may have influenced the use of the term Mach. In the decade preceding human flight, aeronautical engineers referred to the speed of sound as Mach's number, never "Mach 1." In dry air at 20 Celsius, the speed of sound is 340.3 m/s. The speed represented by Mach 1 is not a constant; for example, it is mostly dependent on temperature. Mach number is useful because the fluid behaves in a similar manner at a given Mach number, regardless of other variables. In the following table, "ranges of Mach values" are referred to, not the "pure" meanings of the words "subsonic" and "supersonic".
Mach number
–
An F/A-18 Hornet creating a vapor cone at transonic speed just before reaching the speed of sound
99.
Speed of sound
–
The speed of sound is the distance travelled per unit time by a sound wave as it propagates through an elastic medium. The speed of sound in an ideal gas depends only on its composition. The speed has a weak dependence on pressure in ordinary air, deviating slightly from ideal behavior. In everyday speech, speed of sound refers to the speed of sound waves in air. However, the speed of sound varies to substance: sound travels most slowly in gases; it travels faster in liquids; and faster still in solids. For example, sound travels at 343.2 m/s in air; it travels at 1,484 m/s in water; and at 5,120 m/s in iron. In an exceptionally stiff material such as diamond, sound travels at 12,000 m/s;, around the maximum speed that sound will travel under normal conditions. These different types of waves in solids usually travel at different speeds, as exhibited in seismology. The speed of a sound wave in solids is determined by the medium's compressibility, shear modulus and density. The speed of shear waves is determined only by the solid material's shear modulus and density. The ratio of the speed of an object to the speed of sound in the fluid is called the object's Mach number. Objects moving at greater than Mach1 are said to be traveling at supersonic speeds. In 1709, Rector of Upminster, published a more accurate measure of the speed of sound, at 1,072 Parisian feet per second. Measurements were made of gunshots including North Ockendon church. Thus the speed that the sound had travelled was calculated.
Speed of sound
–
U.S. Navy F/A-18 traveling near the speed of sound. The white halo consists of condensed water droplets formed by the sudden drop in air pressure behind the shock cone around the aircraft (see Prandtl-Glauert singularity).
Speed of sound
–
Pressure-pulse or compression-type wave (longitudinal wave) confined to a plane. This is the only type of sound wave that travels in fluids (gases and liquids)
100.
Natural units
–
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
–
Base units
101.
Continental drift
–
Continental drift is the movement of the Earth's continents relative to each other, thus appearing to "drift" across the ocean bed. The speculation that continents might have'drifted' was first put forward by Abraham Ortelius in 1596. The idea of continental drift has been subsumed by the theory of plate tectonics, which explains how the continents move. In 1858 Antonio Snider-Pellegrini created two maps demonstrating how the African continents might have once fit together. In his Manual of 1863, Dana says "The continents and oceans had their general outline or form defined in earliest time. This did not change places with the continents. This led Mantovani to propose an Expanding Earth theory which has since been shown to be incorrect. Wegener said that of all those theories, Taylor's, although not fully developed, had the most similarities to his own. In the mid-20th century, the theory of continental drift was referred to as the "Taylor-Wegener hypothesis", although this terminology eventually fell out of common use. Alfred Wegener first presented his hypothesis on January 6, 1912. His hypothesis was that the continents had once formed a single landmass, called Pangea, before drifting to their present locations. Wegener was the first to formally publish the hypothesis that the continents had somehow "drifted" apart. Although he presented much evidence for continental drift, he was unable to provide a convincing explanation for the physical processes which might have caused this drift. The Polflucht hypothesis was also found to be implausible. The theory of continental drift was not accepted for many years.
Continental drift
–
Antonio Snider-Pellegrini's Illustration of the closed and opened Atlantic Ocean (1858).
Continental drift
–
Alfred Wegener
102.
Snail
–
Snail is a common name, applied most often to land snails, terrestrial pulmonate gastropod molluscs. Even a marine species have lungs. Snails can be found in a very wide range including ditches, deserts, the abyssal depths of the sea. Although land snails may be more familiar to laymen, marine snails have much greater diversity and a greater biomass. Numerous kinds of snail can also be found in fresh water. Most snails have thousands of tooth-like structures located on a banded ribbon-like tongue called a radula. The radula works like a file, ripping food into small pieces. It weighed exactly 900 g. Named Gee Geronimo, this snail was owned by Christopher Hudson of Hove, East Sussex, UK, was collected in Sierra Leone in June 1976. Gastropods that lack a conspicuous shell are commonly called slugs rather than snails. Other than that there is little morphological difference between slugs and snails. There are however important differences in habitats and behavior. Slugs squeeze themselves under stone slabs, logs or wooden boards lying on the ground. In such retreats they are in less danger from either desiccation, often those also are suitable places for laying their eggs. Slugs as a group are far from monophyletic; biologically speaking "slug" is a term of convenience with taxonomic significance.
Snail
–
Snail
Snail
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Helix pomatia sealed in its shell with a calcareous epiphragm.
Snail
–
Helix aspersa - garden snail
Snail
–
French cooked snails
103.
Walk
–
Walking is one of the main gaits of locomotion among legged animals, is typically slower than running and other gaits. Walking is defined by an ` inverted pendulum' gait in which the body vaults with each step. This applies regardless of the number of limbs - even arthropods, with eight or more limbs, walk. The walk is descended from the Old English wealcan "to roll". In contrast, running begins when both feet are off the ground with each step. This distinction has the status of a formal requirement in competitive walking events. During walking, the centre of mass reaches a maximum height at midstance, while during running, it is then at a minimum. This distinction, however, only holds approximately level ground. For walking up grades above 9 %, this distinction longer holds for some individuals. Running humans and animals may have contact periods greater than 50% of a gait cycle when rounding corners, running uphill or carrying loads. Speed is another factor that distinguishes walking from running. Champion racewalkers can average more than 14 kilometres per hour over a distance of 20 kilometres. An human child achieves independent walking ability at around 11 months old. Brisk exercise of any kind can improve confidence, stamina, energy, weight control and life expectancy and reduce stress. It can also reduce the risk of coronary heart disease, strokes, diabetes, high blood pressure, osteoporosis.
Walk
–
Computer simulation of a human walk cycle. In this model the head keeps the same level at all times, whereas the hip follows a sine curve.
Walk
–
Racewalkers at the World Cup Trials in 1987
Walk
–
Nordic walkers
Walk
–
Walking in Shilda, Georgia.
104.
Sprint runner
–
Sprinting is running over a short distance in a limited period of time. It is used in many sports that incorporate running, typically as a way of avoiding or catching an opponent. In athletics and field, sprints are races over short distances. They are among the oldest running competitions. There are three sprinting events which are currently held at the Summer Olympics and outdoor World Championships: 400 metres. The position differs depending on the start. Alignment is of key importance in producing the optimal amount of force. Ideally the athlete should push off using both legs for maximum force production. Athletes remain in the same lane on the running track with the sole exception of the 400 m indoors. Races up to 100 m are largely focused to an athlete's maximum speed. All sprints beyond this distance increasingly incorporate an element of endurance. It is an indoor world championship event. Biological factors that determine a sprinter's potential include: The 60 metres is normally run indoors, on a straight section of an athletic track. This is roughly the distance can be run with one breath. It is popular for testing in other sports.
Sprint runner
–
Usain Bolt, world record holder in 100 m and 200 m sprints
Sprint runner
–
Start of the women's 60 m at the 2010 World Indoor Championships
Sprint runner
–
Tyson Gay completes a 100m race
Sprint runner
–
A 200 m bend
105.
Usain Bolt
–
Usain St Leo Bolt, OJ, CD is a Jamaican sprinter. Bolt also holds the record as a part of the 4 × 100 metres relay. Bolt is Olympic champion in these three events. Due to achievements in the athletic field, Bolt is widely considered the greatest sprinter of all time. Bolt won the 100 m, 200 m and 4 × 100 m relay at three consecutive Olympic Games. Bolt gained worldwide popularity at the 2008 Beijing Olympics in world record times. He was the first to win 200 m titles. He improved with 9.58 seconds in 2009 -- the biggest improvement since the start of electronic timing. Bolt has twice broken the 200 metres record, setting 19.30 in 2008 and 19.19 in 2009. Bolt has helped Jamaica with the current record being 36.84 seconds set in 2012. Bolt's most successful event is the 200 m, with four World titles. He has stated that he intends to retire after the 2017 World Championships. As a child, he attended Waldensia Primary, where he first began running in the annual national primary-schools' meeting for his parish. By the age of twelve, he had become the school's fastest runner over the 100 distance. Pablo McNeil, Dwayne Jarrett coached Bolt, encouraging him to focus his energy on improving his athletic abilities.
Usain Bolt
–
Bolt at the 2013 World Championships in Athletics.
Usain Bolt
–
Bolt at the Crystal Palace Meeting in 2007
Usain Bolt
–
Bolt trailing behind Gay in the closing stages of the 200 m race, 2007
Usain Bolt
–
Bolt (left) on the podium with his silver medal from the 200 m race in Osaka (2007)
106.
100 metres
–
The 100 metres, or 100-metre dash, is a sprint race in track and field competitions. The shortest common outdoor running distance, it is one of the most popular and prestigious events in the sport of athletics. It has been contested at the Summer Olympics since 1896 for men and since 1928 for women. The reigning 100 m Olympic champion is often named "the fastest runner in the world." The World Championships 100 metres has been contested since 1983. Runners begin in the starting blocks and the race begins when an official fires the starter's pistol. Sprinters typically reach top speed after somewhere between 50–60 m. Their speed then slows towards the finish line. The 10-second barrier has historically been a barometer of fast men's performances, while the best female sprinters take eleven seconds or less to complete the race. The 100 m emerged from the metrication of the 100 yards, a now defunct distance originally contested in English-speaking countries. The event is largely held outdoors as few indoor facilities have a 100 m straight. US women have also dominated the event winning 9 out of 21 times. At the start, some athletes play psychological games such as trying to be last to the starting blocks. A reaction time less than 0.1 s is considered a false start. For many years a sprinter was disqualified if responsible for two false starts individually.
100 metres
–
Start of the 100 metres final at the 2012 Olympic Games.
100 metres
–
Male sprinters await the starter's instructions
100 metres
–
Usain Bolt breaking the world and Olympic records at the 2008 Beijing Olympics
100 metres
–
Christine Arron (left) wins the 100 m at the Weltklasse meeting.
107.
List of world records in athletics
–
World records in athletics are ratified by the International Association of Athletics Federations. Athletics records comprise the best performances in the sports of field, road running and racewalking. Records are kept for all events contested at some others. Unofficial records for some other events are kept by field statisticians. The non-metric track distance for which official records are kept is the mile run. The criteria include: The dimensions of the equipment used must conform to standards. In road events, the course must be accurately measured, by a certified measurer. Except in road events, the performance must be set in a single-sex race. All team members in a relay race must be of the same nationality. Pacemakers are allowed, provided they have not been lapped; lapped athletes must give way. Drug testing immediately after the performance is now required for ratification of a record. Existing records which predate this requirement are still extant. Athletes who are later found to have been on drugs have their performances invalidated. In running events up in horizontal jump events, wind assistance is permitted only up to 2.0 m/s. In running events up to 800 m in distance, photo finish fully automatic timing is required.
List of world records in athletics
–
Usain Bolt beating Tyson Gay and setting a 100 m world record at the 2009 World Championships in Athletics in Berlin.
List of world records in athletics
–
Jürgen Schult beside the indication of his new discus world record, 1986
List of world records in athletics
–
East German women controversially set many world records in the 1970s and 1980s. World record holder Marita Koch maintains her innocence, although released government files detail her drug usage.
108.
Taipei 101
–
The building remained such until the completion of Burj Khalifa in Dubai in 2009. Taipei has the fastest elevator going to the 87th in 49 to 53 seconds. Construction on the 101-story tower finished in 2004. The tower has served ever since its opening. The building was architecturally created as a symbol of the evolution of technology and Asian tradition. Its postmodernist approach to style gives them modern treatments. The tower is designed to withstand earthquakes. A multi-level mall adjoining the tower houses hundreds of stores, restaurants and clubs. The structure appears frequently in travel literature and international media. Taipei 101 is primarily owned by pan-government shareholders. The name, originally planned until 2003, was derived from the name of the owner. The original name in Chinese was Taipei International Financial Center. Taipei 101 comprises 101 floors above ground, well as 5 basement levels. As of 28 it is still the world's largest and highest-use green building. Taipei 101 claimed the official records for the world's largest New Year's Eve countdown clock.
Taipei 101
–
Taipei 101 Tower in August 2008
Taipei 101
–
Base of the tower
Taipei 101
–
Location of Taipei 101's largest tuned mass damper
Taipei 101
–
Tuned mass damper
109.
Saffir-Simpson Hurricane Scale
–
To be classified as a hurricane, a tropical cyclone must have maximum sustained winds of at least 74 mph. The highest classification in Category 5, is reserved with winds exceeding 156 mph. The classifications can provide some indication of the potential damage and flooding a hurricane will cause upon landfall. Other areas use different scales to label these storms, which are called "cyclones" or "typhoons", depending on the area. While performing the study, Saffir realized there was no simple scale for describing the likely effects of a hurricane. Mirroring the utility of the Richter scale in describing earthquakes, he devised a 1 -- 5 scale based on speed that showed expected damage to structures. Simpson added the effects of storm flooding. The new scale became operational on May 15, 2010. Likewise, an intensity of 135 knots is 250.02 km/h, which according to the definition used before the change would be Category 5. The new scale became operational on May 15, 2012. The scale separates hurricanes into five different categories based on wind. Central surge values are approximate and often dependent on other factors, such as the size of the storm and the location. Intensity of example hurricanes is from both the time of landfall and the maximum intensity. As a result, it is not uncommon for a pressure to be significantly higher or lower than expected for a specific category. Generally, large storms with very large radii of maximum winds have the lowest pressures relative to its intensity.
Saffir-Simpson Hurricane Scale
–
Hurricane Barbara in 2013 making landfall.
Saffir-Simpson Hurricane Scale
–
Juan in 2003 approaching Nova Scotia
Saffir-Simpson Hurricane Scale
–
Hurricane Isidore near its landfall on the Yucatán peninsula
Saffir-Simpson Hurricane Scale
–
Daniel in the eastern Pacific
110.
Autoroutes of France
–
The Autoroute system in France consists largely of toll roads, except around large cities and in parts of the north. It is a network of 11,882 km worth of motorways in 2014. Autoroute destinations are shown in blue, while destinations reached through a combination of autoroutes are shown with an added autoroute logo. Toll autoroutes are signalled with the word péage. Unlike other motorway systems, there is no systematic numbering system, but there is a clustering of Autoroute numbers based on region. A1, A3, A4, A5, A6, A10, A13, A14, A15, A16 radiate from Paris with A2, A11, A12 branching from A1, A10, A13, respectively. A7 begins in Lyon, where A6 ends. A8 and A9 begin respectively near Aix-en-Provence and Avignon. The 20s are found in northern France. The 30s are found in eastern France. The 40s are found near the Alps. The 50s are near the French Riviera. The 60s are found in southern France. The 70s are found in the centre of the country. The 80s are found west of Paris.
Autoroutes of France
–
Toll barrier in Toulouse-Sud (south of Toulouse), on autoroute A61
Autoroutes of France
Autoroutes of France
–
The French Autoroute A1
Autoroutes of France
–
A French motorway.
111.
Recumbent bicycle
–
A recumbent bicycle is a bicycle that places the rider in a laid-back reclining position. Most recumbent riders choose this type of design for ergonomic reasons; the rider's weight is distributed comfortably over a larger area, supported by back and buttocks. On a traditional bicycle, the weight rests entirely on a small portion of the sitting bones, the hands. Most recumbent models also have an aerodynamic advantage; the reclined, legs-forward position of the rider’s body presents a smaller frontal profile. A variant with three wheels is a recumbent tricycle. Recumbents can be categorized by their wheelbase, unfaired, front-wheel or rear-wheel drive. Within these categories are variations, intermediate types, even convertible designs – there is no "standard" recumbent. Larger diameter wheels generally have lower rolling resistance but a higher profile leading to higher air resistance. Another advantage of both wheels being the same size is that the bike requires only one size of inner tube. One common arrangement is an ISO 559 rear wheel and an ISO 406 or ISO 451 front wheel. A front-wheel configuration also overcomes strike since the pedals and front wheel turn together. PBFWD bikes may have dual 26-inch wheels or larger. Steering for recumbent bikes can be generally categorized as over-seat or above seat steering; under-seat; or center steering or pivot steering. Chopper-style bars are sometimes seen on LWB bikes. USS is usually indirect -- the bars link through a system of possibly a crank.
Recumbent bicycle
–
Bacchetta Corsa, a short-wheelbase high racer
Recumbent bicycle
–
A RANS V2 Formula long-wheelbase recumbent bike fitted with a front fairing
Recumbent bicycle
–
Woman riding a Cruzbike Sofrider (PBFWD recumbent) near the end of the 500-mile (800 km) "Ride Across North Carolina" 2007
Recumbent bicycle
–
Long-wheel-base low-rider recumbent with steering u-joint (UA)
112.
Paintball marker
–
A paintball marker, also known as a paintball gun, is the main piece of equipment in the sport of paintball. Markers use an expanding gas, such as carbon dioxide or compressed air, to propel paintballs through the barrel. The term "marker" is derived from its original use as a means for forestry personnel to mark trees and ranchers to mark wandering cattle. The muzzle velocity of paintball markers is approximately 90 m/s. While greater muzzle velocity is possible, it has been ruled unsafe for use on most commercial paintball fields. However, the damage depends on the paintball's velocity, its impact angle, which part of the body it hits. Most paintball markers have four main components: the body, hopper, gas system, barrel. Paintball markers fall into two main categories in terms of mechanism - mechanical and electropneumatic. Mechanically operated paintball markers operate using solely mechanical means, as such do not use electro-pneumatic solenoids controlled by an electronic board to fire. Markers of this type are the oldest used in the sport as the first ever game of paintball was played using the bolt-action Nelspot pistol. To cock the mechanism, the bolt is pulled backwards thus opening the breech and loading a paintball. Doing so also pulls the hammer backwards against the main spring, then held back by a sear connected to the trigger. The bolt is then pushed forward, which loads the paintball into the barrel and the marker is ready to fire. Notable examples of markers which operate in this way include the Sheridan K2, the Worr Games Products Sniper and the Chipley Custom Machine S6. Nelson Valve: Named after the Nelson Paint Company whose marker, the Nelspot 007, first employed this mechanism.
Paintball marker
–
The Planet Eclipse Ego, an electropneumatic paintball marker
Paintball marker
–
Spyder VS2 Paintball Marker
Paintball marker
–
A player using a Spyder paintball marker
Paintball marker
–
A CO 2 tank
113.
Boeing 747-8
–
The Boeing 747-8 is a wide-body jet airliner developed by Boeing Commercial Airplanes. Officially announced in 2005, the 747-8 is the third generation of the 747, with lengthened fuselage, improved efficiency. The 747-8 is the largest 747 version, the longest passenger aircraft in the world. The 747-8 is offered in the 747-8 Freighter for cargo. The first 747-8F performed the model's maiden flight on February 8, 2010, following on March 20, 2011. The passenger model began deliveries in 2012. As of November 2016, confirmed orders for the 747-8 total 138: 50 of the passenger version. Boeing had considered larger-capacity versions of the 747 several times during the 2000s. In 2000, Boeing offered the 747X and 747X Stretch derivatives to the Airbus A3XX. This was a more modest proposal than the previous − 500X and 600X. The 747X would increase the 747's wingspan by adding a segment at the root. The 747X was to carry 430 passengers up to nmi. The 747X Stretch would be extended to ft long, allowing it to carry 500 passengers up to 7,800 nmi. However, the 747X family was unable to attract enough interest to enter production. Some of the ideas developed for the 747X were used on the 747-400ER.
Boeing 747-8
–
Boeing 747-8
Boeing 747-8
–
Boeing's Everett Facility at Paine Field, originally built for the 747 program, is the site of 747-8 assembly.
Boeing 747-8
–
The 747-8 landing gear configuration is the same as on earlier 747 versions
Boeing 747-8
–
Boeing 747-8 flight deck
114.
Land speed record
–
The land speed record is the highest speed achieved by a person using a vehicle on land. The record is standardized as the speed over a course of fixed length, averaged over two runs. There are numerous other class records for cars; motorcycles fall into a separate class. The first regulators were the Automobile Club de France, who proclaimed themselves arbiters of the record in about 1902. Regional auto clubs had to ensure records would be recognized. The AIACR became the FIA in 1947. No holder of the absolute record since has been wheel-driven. She drove a 100 hp development of the K5, in Blackpool. Through her career as a stuntwoman, she met high-speed car designer who built the "Motivator" vehicle. Craig Breedlove's mark of 407.447 miles per hour, set in Spirit of America in September 1963, was initially considered unofficial. Some time later, the Fédération Internationale de Motocyclisme created a non-wheel-driven category, ratified Spirit of America's time for this mark. On July 1964, Donald Campbell's Bluebird CN7 posted a speed of 403.10 miles per hour on Australia. This became the official FIA LSR, although Campbell was disappointed not to have beaten Breedlove's time. In October, four-wheel jet-cars were eligible for neither FIA nor FIM ratification. No wheel-driven car has since held the absolute record.
Land speed record
–
ThrustSSC, driven by Royal Air Force pilot Andy Green, holds the land speed record.
Land speed record
–
Ralph DePalma in his Packard '905' Special at Daytona Beach in 1919
Land speed record
–
Dorothy Levitt, in a 26hp Napier, at Brooklands, England, in 1908
115.
Kelvins
–
The kelvin is a unit of measure for temperature based upon an absolute scale. It is assigned the unit symbol K. The kelvin is defined as the fraction.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 of the need for an "absolute thermometric scale". Unlike degree Celsius, the kelvin is not referred to or 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 scale. When spoken, the unit is pluralised using the same 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 adjectivally to modify the noun "scale" and is capitalized. As with most other unit symbols there is a space between the numeric value and the kelvin symbol. Before the 13th CGPM in 1967 -- 1968, the kelvin was called a "degree", 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".
Kelvins
–
Lord Kelvin, the namesake of the unit
Kelvins
–
A thermometer calibrated in degrees Celsius (left) and kelvins (right).
116.
Cartridge (weaponry)
–
Military and commercial producers continue to pursue the goal of caseless ammunition. A cartridge without a bullet is called a blank. One, completely inert is called a dummy. Some artillery ammunition uses the same cartridge concept as found in small arms. In other cases, the artillery shell is separate from the propellant charge. In popular use, the term "bullet" is often misused to refer to a complete cartridge. The cartridge case seals a firing chamber in all directions excepting the bore. A firing pin strikes the primer and ignites it. The primer compound deflagrates; it does not detonate. A jet of burning gas from the primer ignites the propellant. Gases from the powder expand the case to seal it against the wall. These propellant gases push on the bullet base. In response to this pressure, the bullet will move in the path of least resistance, down the bore of the barrel. After the bullet leaves the barrel, the chamber pressure drops to atmospheric pressure. The case, elastically expanded by chamber pressure, contracts slightly.
Cartridge (weaponry)
–
A variety of rifle cartridges: (1).17HM2 (2).17HMR (3) .22LR (4).22 Win Mag R/F.22 WMR (5).17/23 SMc (6) 5mm/35 SMc (7) .22 Hornet (8) .223 Remington (9) .223 WSSM (10) .243 Win (11) P.O. Ackley#Wildcats & Ackley Improved Cartridges.243 Win Improved (Ackley) (12).25-06 Rem (13).270 Win (14) .308 Win (15) .30-06 Springfield (16) .45-70 Government (17) .50-90 Sharps
Cartridge (weaponry)
–
Historic British cartridges
Cartridge (weaponry)
–
Chassepot paper cartridge (1866).
Cartridge (weaponry)
–
(From Left to Right): A .577 Snider cartridge (1867), a .577/450 Martini-Henry cartridge (1871), a later drawn brass.577/450 Martini-Henry cartridge, and a .303 British Mk VII SAA Ball cartridge.
117.
Soviet Union
–
A union of multiple subnational Soviet republics, economy were highly centralized. The Soviet Union was a one-party federation, governed by the Communist Party as its capital. They established the Russian Socialist Federative Soviet Republic, beginning a civil war between the counter-revolutionary "Whites." In 1922, the Communists were victorious, forming the Soviet Union with the unification of the Russian, Transcaucasian, Ukrainian, Byelorussian republics. Following Lenin's death in 1924, a brief power struggle, Joseph Stalin came to power in the mid-1920s. Stalin initiated a centrally planned command economy. Shortly before World War II, Stalin signed the non-aggression pact with Nazi Germany, after which the two countries invaded Poland in September 1939. In June 1941 the Germans invaded, opening the largest and bloodiest theater of war in history. Soviet forces eventually captured Berlin in 1945. The territory overtaken by the Red Army became satellite states of the Eastern Bloc. The Cold War emerged as the Soviet bloc confronted the Western states that united in the North Atlantic Treaty Organization in 1949. Following Stalin's death in 1953, a period of economic liberalization, known as "de-Stalinization" and "Khrushchev's Thaw", occurred under the leadership of Nikita Khrushchev. The country developed rapidly, as millions of peasants were moved into industrialized cities. The USSR took an early lead with the first ever satellite and the first human spaceflight. The war was matched by an escalation of American military aid to Mujahideen fighters.
Soviet Union
–
Vladimir Lenin addressing a crowd with Trotsky, 1920
Soviet Union
–
Flag
Soviet Union
–
Stalin and Nikolai Yezhov, head of the NKVD. After Yezhov was executed, he was edited out of the image.
Soviet Union
118.
Flight airspeed record
–
An air speed record is the highest airspeed attained by an aircraft of a particular class. The rules for all official aviation records are defined by Fédération Aéronautique Internationale, which also ratifies any claims. Speed records are divided with sub-divisions. There are three classes of aircraft: amphibians; then within these classes, there are records for aircraft in a number of weight categories. There are still further sub-divisions for piston-engined, turbojet, turboprop, aircraft. Within each of these groups, records are defined for closed circuits of various sizes carrying various payloads. Records in "gray" font color are unofficial, including unpublicized secrets. The Lockheed SR-71 Blackbird holds the official Air Speed Record for a airbreathing jet aircraft with a speed of 3,530 km/h. It was capable of landing unassisted on conventional runways. The record was set on 28 July 1976 by Eldon W. Joersz and George T. Morgan Jr. near California, US. The secrecy, of World War II meant that new speed breakthroughs were not publicized nor ratified. In October 1941, an unofficial record of 1004 km/h was secretly set by a Messerschmitt Me 163 AV4 rocket aircraft. Continued research during the war extended the secret, unofficial speed record to 1130 km/h by July 1944, achieved by a Messerschmitt Me 163B V18. The new official record in the post-war period was achieved by a Gloster Meteor in November 1945, at 976 km/h. The first aircraft to exceed the unofficial October 1941 record of the Me 163 AV4 was the Douglas Skystreak, which achieved 1031 km/h in August 1947.
Flight airspeed record
–
The SR-71 Blackbird is the current record-holder for a manned airbreathing jet aircraft.
119.
Lockheed SR-71 Blackbird
–
The Lockheed SR-71 "Blackbird" was a long-range, Mach 3+ strategic reconnaissance aircraft, operated by the United States Air Force. It was developed as a black project from the Lockheed A-12 reconnaissance aircraft in the 1960s by Lockheed and its Skunk Works division. American aerospace engineer Clarence "Kelly" Johnson was responsible for many of the design's innovative concepts. During aerial reconnaissance missions, the SR-71 operated at high speeds and altitudes to allow it to outrace threats. If a surface-to-air missile launch was detected, the standard evasive action was simply to accelerate and outfly the missile. The SR-71 was designed with a reduced radar cross-section. The SR-71 served with the U.S. Air Force from 1964 to 1998. A total of 32 aircraft were built; 12 were lost in accidents and none lost to enemy action. The SR-71 has been given several nicknames, including Blackbird and Habu. It has held the world record for the fastest air-breathing manned aircraft since 1976; this record was previously held by the related Lockheed YF-12. Lockheed's previous reconnaissance aircraft was the relatively slow U-2, designed for the Central Intelligence Agency. In late 1957, the CIA approached the defense contractor Lockheed to build an undetectable spy plane. The project, named Archangel, was led by Kelly Johnson, head of Lockheed's Skunk Works unit in Burbank, California. The work on project Archangel began in the second quarter of 1958, with aim of flying higher and faster than the U-2. Out of 11 successive designs drafted in a span of 10 months, "A-10" was the front runner.
Lockheed SR-71 Blackbird
–
SR-71 "Blackbird"
Lockheed SR-71 Blackbird
–
SR-71 Blackbird assembly line at Skunk Works
Lockheed SR-71 Blackbird
–
The flight instrumentation of an SR-71's cockpit
Lockheed SR-71 Blackbird
–
A Lockheed M-21 with D-21 drone on top
120.
Space shuttle
–
The first of four orbital test flights occurred in 1981, leading to operational flights beginning in 1982. Five Shuttle systems were used on a total of 135 missions from 1981 to 2011, launched from the Kennedy Space Center in Florida. The Shuttle fleet's total time was 1322 days, 19 hours, 23 seconds. Shuttle components included the expendable external tank containing liquid hydrogen and liquid oxygen. At the conclusion of the mission, the orbiter fired its OMS to de-orbit and re-enter the atmosphere. After landing at Edwards, the orbiter was flown back on a specially modified Boeing 747. Enterprise, had no orbital capability. Four fully operational orbiters were initially built: Columbia, Challenger, Discovery, Atlantis. Of these, two were lost in mission accidents: Challenger in 1986 and Columbia in 2003, with a total of fourteen astronauts killed. A fifth operational orbiter, Endeavour, was built in 1991 to replace Challenger. The Space Shuttle was retired on July 21, 2011. Nixon's post-Apollo NASA budgeting withdrew support of all system components except the Shuttle, to which NASA applied the STS name. The vehicle consisted with reusable solid booster rockets. The first of four orbital test flights occurred in 1981, leading beginning in 1982, all launched from Florida. The system was retired with Atlantis making the final launch of the three-decade Shuttle program on July 8, 2011.
Space shuttle
–
Discovery lifts off at the start of STS-120.
Space shuttle
–
STS-129 ready for launch
Space shuttle
–
President Nixon (right) with NASA Administrator Fletcher in January 1972, three months before Congress approved funding for the Shuttle program
Space shuttle
–
STS-1 on the launch pad, December 1980
121.
Escape velocity
–
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
–
Luna 1, launched in 1959, was the first man-made object to attain escape velocity from Earth (see below table).
Escape velocity
–
General
122.
Voyager 1
–
Voyager 1 is a space probe launched by NASA on September 5, 1977. Part of the Voyager program to study the outer Solar System, Voyager 1 launched 16 days after Voyager 2. Having operated for 39 years, 16 days, the spacecraft still communicates with the Deep Space Network to receive routine commands and return data. The probe's primary mission objectives included Saturn's large moon, Titan. Voyager was the first probe to provide detailed images of their moons. On August 2012, Voyager 1 crossed the heliopause to become the first spacecraft to enter interstellar space and study the interstellar medium. In the 1960s, a Grand Tour to study the outer planets was proposed which prompted NASA to begin work on a mission in the early 1970s. Information gathered by the Pioneer 10 spacecraft helped Voyager's engineers design Voyager to cope more effectively with the intense environment around Jupiter. Initially, Voyager 1 was planned as "Mariner 11" of the Mariner program. Due to budget cuts, the mission was renamed the Mariner Jupiter-Saturn probes. As the program progressed, the name was later changed to Voyager, since the probe designs began to differ greatly from previous Mariner missions. Voyager 1 was constructed by the Jet Propulsion Laboratory. Voyager has 16 hydrazine thrusters, referencing instruments to keep the probe's radio antenna pointed toward Earth. Collectively, these instruments are Articulation Control Subsystem, along with redundant units of most instruments and 8 backup thrusters. The spacecraft also included 11 scientific instruments to study celestial objects such as planets as it travels through space.
Voyager 1
–
Voyager 1, artist's impression
Voyager 1
Voyager 1
Voyager 1
–
Voyager 1 lifted off with a Titan IIIE
123.
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.
124.
Helios (spacecraft)
–
Helios-A and Helios-B, are a pair of probes launched into heliocentric orbit for the purpose of studying solar processes. A joint venture of West Germany's space agency DFVLR and NASA, the probes were launched from Cape Canaveral, Florida, on Dec. 10, 1974, Jan. 15, 1976, respectively. Built as the main contractor they were the first spaceprobes built outside the United States or Soviet Union. The probes are notable for having set a maximum record among spacecraft at 252,792 km/h. Helios 2 was sent into orbit 13 months after the launch of Helios 1. They continued to send data up to 1985. The probes still remain in their elliptical orbits around the Sun. The two Helios probes look very similar. The central body is a sixteen-sided prism 1.75 m in 0.55 meters high. Most of the instrumentation is mounted in this central body. Exceptions are small telescopes that measure the zodiacal light that emerge from the central body. Two solar panels extend above and below the central body, giving the assembly the appearance of a diabolo or spool of thread. At launch the probe reaches a maximum diameter of 2.77 meters. Once in orbit, a antenna unfolded on top of the probe and increased the total height to 4.20 meters.
Helios (spacecraft)
–
Prototype of the Helios spacecraft
Helios (spacecraft)
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Helios-A sitting atop the Titan IIIE / Centaur launch vehicle.
Helios (spacecraft)
–
Current
Helios (spacecraft)
125.
Heliocentric orbit
–
A heliocentric orbit is an orbit around the barycenter of the Solar System, usually located within or very near the surface of the Sun. All planets, asteroids in the Solar System are in such orbits, as are many artificial probes and pieces of debris. The moons of planets in the Solar System, by contrast, are not in heliocentric orbits as they orbit their respective planet. A similar phenomenon allows the detection of exoplanets by way of the radial method. The helio- prefix is derived from the Greek word helios, meaning "sun", also Helios, the personification of the Sun in Greek mythology. Low-energy transfer windows open up which allow movement between planets with the lowest possible delta-v requirements. Transfer injections can place spacecraft into either bi-elliptic transfer orbit. Earth's orbit Geocentric orbit Heliocentrism Astrodynamics Low-energy transfer List of artificial objects in heliocentric orbit List of orbits
Heliocentric orbit
–
The BepiColombo heliocentric cruise will use gravity assists around the Earth, Venus and Mercury and will last 6 years
126.
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
127.
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
128.
Jean Piaget
–
Jean Piaget was a Swiss clinical psychologist known for his pioneering work in child development. Piaget's theory of cognitive development and view are together called "genetic epistemology". Piaget placed great importance on the education of children. Piaget's research influenced several people. His theory of development is studied in pre-service education programs. Educators continue to incorporate constructionist-based strategies. According to Ernst von Glasersfeld, Jean Piaget was "the great pioneer of the constructivist theory of knowing." However, his ideas did not become widely popularized until the 1960s. This then led as a major sub-discipline in psychology. By the end of the 20th century, Piaget was second only to B. F. Skinner as the most cited psychologist of that era. Piaget was born in the Francophone region of Switzerland. He was the oldest son of Arthur Piaget, Rebecca Jackson. Piaget was a precocious child who developed an interest in the natural world. He was studied briefly at the University of Zürich. During this time, he published two philosophical papers which he later dismissed as adolescent thought.
Jean Piaget
–
Bust of Jean Piaget in the Parc des Bastions, Geneva
Jean Piaget
–
Photo of the Jean Piaget Foundation with Pierre Bovet (1878–1965) first row (with large beard) and Jean Piaget (1896–1980) first row (on the right, with glasses) in front of the Rousseau Institute (Geneva), 1925
129.
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
–
Einstein at the age of 3 in 1882
Albert Einstein
–
Albert Einstein in 1893 (age 14)
Albert Einstein
–
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)
130.
Air speed
–
Airspeed is the speed of an aircraft relative to the air. Among the common conventions for qualifying airspeed are: indicated airspeed, calibrated airspeed, true airspeed, density airspeed. During cruising flight at altitudes, temperatures common for airliners, the four speeds trace a shape that looks like the mathematical square root symbol. The indication of airspeed is ordinarily accomplished on board an aircraft by an airspeed indicator connected to a pitot-static system. These two pressures are compared by the ASI to give an IAS reading. Indicated airspeed is the airspeed reading uncorrected for instrument, position, other errors. Outside the Soviet bloc, most airspeed indicators show the speed in knots. Some light aircraft have airspeed indicators showing speed in kilometers per hour. An airspeed indicator is a differential gauge with the pressure reading expressed in units of speed, rather than pressure. The airspeed is derived from the pitot tube, or stagnation pressure, the static pressure. The tube is mounted facing forward; the static pressure is frequently detected at static ports on one or both sides of the aircraft. Sometimes both pressure sources are combined in a pitot-static tube. The correction for this error varies for different aircraft and airspeeds. Further errors of 10% or more are common if the airplane is flown in “uncoordinated” flight. Calibrated airspeed is indicated airspeed corrected for instrument errors, installation errors.
Air speed
–
Aircraft have pitot tubes for measuring airspeed
Air speed
–
An airspeed indicator is a flight instrument that displays airspeed. This airspeed indicator has standardized markings for a multiengine airplane
131.
List of vehicle speed records
–
The following is a list of speed records for various categories of vehicles. Note significant figures: unless otherwise indicated, trailing zeros to the left of a decimal point are not significant. ^ Mach number depends on ambient temperature, thus altitude, well as speed; it is not a direct measure of speed. ^ Unofficial speed records by the Sikorsky X2 and the Eurocopter X3 would surpass this record if accepted. In order to unambiguously express the speed of a spacecraft, a frame of reference must be specified. Velocities in different frames of reference are not directly comparable; the matter of the "fastest spacecraft" depends on the frame. Because of the influence of gravity, maximum velocities are usually attained to a massive body. Orders of magnitude
List of vehicle speed records
–
ThrustSSC, which has held the land speed record since 15 October 1997
List of vehicle speed records
–
Lt. Col. John P. Stapp rides the rocket sled at Edwards Air Force Base
List of vehicle speed records
–
Sunswift IV, the world's fastest solar-powered land vehicle, during its world record run
List of vehicle speed records
–
VeloX3, the world's fastest human-powered vehicle, is prepared for a run during the 2013 World Human Powered Speed Challenge
132.
Projectile
–
A projectile is any object thrown into space by the exertion of a force. Although any object in motion through space may be called a projectile, the term more commonly refers to a ranged weapon. Mathematical equations of motion are used to analyze projectile trajectory. Pneumatic rifles use compressed gases, while most other guns and cannons utilize expanding gases liberated by sudden chemical reactions. Light-gas guns use a combination of these mechanisms. Railguns utilize greatly increasing the muzzle velocity. Some projectiles provide propulsion by means of a rocket engine or jet engine. In military terminology, a rocket is unguided, while a missile is guided. Note the two meanings of "rocket": an ICBM is a guided missile with a engine. An explosion, whether or not by a weapon, causes the debris to act as high velocity projectiles. Device may also be designed to produce many high velocity projectiles by the break-up of its casing, these are correctly termed fragments. E.g. shells, may carry an explosive charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause special damage, poisoning. See bowling. Kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, somewhat pointed ones such as bullets.
Projectile
–
Projectile and cartridge case for the massive World War II German 80cm Schwerer Gustav railway gun
Projectile
–
Ball speeds of 105 miles per hour (169 km/h) have been recorded in baseball.
133.
V speeds
–
In aviation, V-speeds are standard terms used to define airspeeds important or useful to the operation of all aircraft. Using them is considered a best practice to maximize both. The actual speeds represented by these designators are specific to a particular model of aircraft. These are the stalling speeds for the aircraft at its maximum weight. Proper display of V speeds is an airworthiness requirement for type-certificated aircraft in most countries. The most common V-speeds are often defined by a particular government's aviation regulations. In the United States, these are FARs. In Canada, the regulatory body, Transport Canada, defines 26 commonly used V-speeds in their Aeronautical Information Manual. V-speed definitions in equivalent are for certification of airplanes, not for their operational use. The descriptions below are for use by pilots. These V-speeds are defined by regulations. Some of the descriptions provided are simplified. Some of these V-speeds are specific to particular types of aircraft and are not defined by regulations. V1 is takeoff speed. It is the speed above which the takeoff will continue even if an engine fails or another problem occurs, such as a blown tire.
V speeds
–
A single-engine Cessna 150L's airspeed indicator indicating its V speeds.
V speeds
–
A flight envelope diagram showing V S (stall speed at 1G), V C (corner/maneuvering speed) and V D (dive speed)
134.
Richard Feynman
–
For his contributions to the development of quantum electrodynamics, Feynman, jointly with Sin ` ichirō Tomonaga, received the Nobel Prize in Physics in 1965. Feynman developed a widely used pictorial scheme for the mathematical expressions governing the behavior of subatomic particles, which later became known as Feynman diagrams. During his lifetime, Feynman became one of the best-known scientists in the world. In addition to his work in theoretical physics, Feynman has been credited with introducing the concept of nanotechnology. He held the Richard C. Tolman professorship in theoretical physics at the California Institute of Technology. By his youth Feynman described himself as an "avowed atheist". Like Edward Teller, Feynman was a late talker, by his third birthday had yet to utter a single word. He retained a Brooklyn accent as an adult. From his mother he gained the sense of humor that he had throughout his life. As a child, he had a talent for engineering, delighted in repairing radios. When he was in school, he created a home burglar alarm system while his parents were out for the day running errands. Four years later, the family moved to Far Rockaway, Queens. Though separated by nine years, Joan and Richard were close, as they both shared a natural curiosity about the world. Their mother thought that women did not have the cranial capacity to comprehend such things.
Richard Feynman
–
Richard Feynman
Richard Feynman
–
Feynman (center) with Robert Oppenheimer (right) relaxing at a Los Alamos social function during the Manhattan Project
Richard Feynman
–
The Feynman section at the Caltech bookstore
Richard Feynman
–
Mention of Feynman's prize on the monument at the American Museum of Natural History in New York City. Because the monument is dedicated to American Laureates, Tomonaga is not mentioned.
135.
The Feynman Lectures on Physics
–
The lectures were given during 1961 -- 1963. The book's authors are Feynman, Robert B. Leighton, Matthew Sands. The book comprises three volumes. The first volume focuses on mechanics, radiation, heat, including relativistic effects. The second volume is mainly on electromagnetism and matter. The third volume is on quantum mechanics; it shows, for example, how the double-slit experiment contains the essential features of quantum mechanics. The book also includes chapters on mathematics and the relation of physics to other sciences. The Feynman Lectures on Physics is perhaps the most popular physics book ever written. It has been printed in a dozen languages. More than million copies have probably even more copies in foreign-language editions. A 2013 review in Nature described the book as having "beauty, unity... presented with insight." In 2013, Caltech in cooperation with The Feynman Lectures Website made the book freely available, on the feynmanlectures.caltech.edu. By 1960, discoveries in physics had resolved a number of troubling inconsistencies in fundamental theories. In particular, it was his work in quantum electrodynamics for which he was awarded the 1965 Nobel Prize in physics.
The Feynman Lectures on Physics
–
The Feynman Lectures on Physics including Feynman's Tips on Physics: The Definitive and Extended Edition (2nd edition, 2005)
The Feynman Lectures on Physics
–
Feynman the “Great Explainer”: The Feynman Lectures on Physics found an appreciative audience beyond the undergraduate community.
136.
Addison-Wesley
–
Addison-Wesley is a publisher of textbooks and computer literature. It is an imprint of Pearson PLC, education company. In addition to publishing books, Addison-Wesley also distributes its technical titles through the Safari Books Online e-reference service. Addison-Wesley's majority of sales derive from the United States and Europe. The Addison-Wesley Professional Imprint produces content including eBooks, video for the professional IT worker including developers, programmers, managers, system administrators. Classic titles include The Art of Computer Programming, The C++ Programming Language, Design Patterns. Addison-Wesley Professional is also a partner with Safari Books Online. Its first book was Programs for an Electronic Digital Computer, by Wilkes, Wheeler, Gill. In 1977, Addison-Wesley merged it with the Cummings division of the company to form Benjamin Cummings. It became part of Addison Wesley Longman in 1994. The trade division of Addison-Wesley was sold to Perseus Books Group in 1997, leaving Addison-Wesley as solely an educational publisher. Pearson moved the former Addison Wesley Longman offices to Boston in 2004. Its current executives hail with a storied history of their own. Leighton, Matthew Sands Concrete Mathematics: A Foundation For Computer Science by Ronald Graham, Donald Knuth, Oren Patashnik Evolutionary Biology by Dr. Eli C. Exploratory data analysis by John W. Tukey, based on a course taught at Princeton.
Addison-Wesley
–
Addison-Wesley
137.
Integral
–
In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, other concepts that arise by combining infinitesimal data. Integration is one of the two main operations of calculus, with its inverse, differentiation, being the other. The area above the x-axis adds to the total and that below the x-axis subtracts from the total. Roughly speaking, the operation of integration is the reverse of differentiation. For this reason, the integral may also refer to the related notion of a function F whose derivative is the given function f. In this case, it is called an indefinite integral and is written: F = ∫ f d x. The integrals discussed in this article are those termed definite integrals. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a region by breaking the region into vertical slabs. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space. A similar method was independently developed in China around the 3rd century AD by Liu Hui, who used it to find the area of the circle. This method was later used by father-and-son mathematicians Zu Chongzhi and Zu Geng to find the volume of a sphere. The next significant advances in integral calculus did not begin to appear until the 17th century. Further steps were made in the 17th century by Barrow and Torricelli, who provided the first hints of a connection between differentiation. Barrow provided the first proof of the fundamental theorem of calculus.
Integral
–
A definite integral of a function can be represented as the signed area of the region bounded by its graph.
138.
Absement
–
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
–
Ryan Janzen, playing with Hart House Symphonic Band
Absement
–
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
–
Aquatune Hydraulophone at the main entrance to the Legoland waterpark in Carlsbad California. This hydraulophone is in the shape of giant lego blocks.
Absement
–
Hot tub hydraulophone
139.
Jerk (physics)
–
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)
–
Timing diagram over one rev. for angle, angular velocity, angular acceleration, and angular jerk
140.
SI units
–
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
–
The seven base units in the International System of Units
SI units
–
Carl Friedrich Gauss
SI units
–
Thomson
141.
Second
–
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
–
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
–
Key concepts
142.
Area
–
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
–
A square metre quadrat made of PVC pipe.
Area
–
The combined area of these three shapes is approximately 15.57 squares.
143.
Square metre
Square metre
–
Comparison of 1 Square metre with some Imperial and metric units of area
144.
Angle
–
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
–
An angle enclosed by rays emanating from a vertex.
145.
Radian
–
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
–
A chart to convert between degrees and radians
Radian
–
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.
146.
Solid angle
–
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.
147.
Steradian
–
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.
148.
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
149.
Hertz
–
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
–
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
–
A sine wave with varying frequency
150.
Kinematic viscosity
–
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
–
Pitch has a viscosity approximately 230 billion (2.3 × 10 11) times that of water.
Kinematic viscosity
–
A simulation of substances with different viscosities. The substance above has lower viscosity than the substance below
Kinematic viscosity
–
Example of the viscosity of milk and water. Liquids with higher viscosities make smaller splashes when poured at the same velocity.
Kinematic viscosity
–
Honey being drizzled.
151.
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
–
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.
152.
Kilogram square metre
–
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
–
Tightrope walker Samuel Dixon using the long rod's moment of inertia for balance while crossing the Niagara River in 1890.
Kilogram square metre
–
Flywheels have large moments of inertia to smooth out mechanical motion. This example is in a Russian museum.
Kilogram square metre
–
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
–
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.
153.
List of equations in classical mechanics
–
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
–
Kinematic quantities of a classical particle: mass m, position r, velocity v, acceleration a.
154.
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
155.
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
156.
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
157.
Newton metre
Newton metre
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Conversion factors [edit]