1.
Physics
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Physics is the natural science that involves the study of matter and its motion and behavior through space and time, along with related concepts such as energy and force. One of the most fundamental disciplines, the main goal of physics is to understand how the universe behaves. Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy, Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the mechanisms of other sciences while opening new avenues of research in areas such as mathematics. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs, the United Nations named 2005 the World Year of Physics. Astronomy is the oldest of the natural sciences, the stars and planets were often a target of worship, believed to represent their gods. While the explanations for these phenomena were often unscientific and lacking in evidence, according to Asger Aaboe, the origins of Western astronomy can be found in Mesopotamia, and all Western efforts in the exact sciences are descended from late Babylonian astronomy. The most notable innovations were in the field of optics and vision, which came from the works of many scientists like Ibn Sahl, Al-Kindi, Ibn al-Haytham, Al-Farisi and Avicenna. The most notable work was The Book of Optics, written by Ibn Al-Haitham, in which he was not only the first to disprove the ancient Greek idea about vision, but also came up with a new theory. In the book, he was also the first to study the phenomenon of the pinhole camera, many later European scholars and fellow polymaths, from Robert Grosseteste and Leonardo da Vinci to René Descartes, Johannes Kepler and Isaac Newton, were in his debt. Indeed, the influence of Ibn al-Haythams Optics ranks alongside that of Newtons work of the same title, the translation of The Book of Optics had a huge impact on Europe. From it, later European scholars were able to build the devices as what Ibn al-Haytham did. From this, such important things as eyeglasses, magnifying glasses, telescopes, Physics became a separate science when early modern Europeans used experimental and quantitative methods to discover what are now considered to be the laws of physics. Newton also developed calculus, the study of change, which provided new mathematical methods for solving physical problems. The discovery of new laws in thermodynamics, chemistry, and electromagnetics resulted from greater research efforts during the Industrial Revolution as energy needs increased, however, inaccuracies in classical mechanics for very small objects and very high velocities led to the development of modern physics in the 20th century. Modern physics began in the early 20th century with the work of Max Planck in quantum theory, both of these theories came about due to inaccuracies in classical mechanics in certain situations. Quantum mechanics would come to be pioneered by Werner Heisenberg, Erwin Schrödinger, from this early work, and work in related fields, the Standard Model of particle physics was derived. Areas of mathematics in general are important to this field, such as the study of probabilities, in many ways, physics stems from ancient Greek philosophy
2.
Position (vector)
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Usually denoted x, r, or s, it corresponds to the straight-line distances along each axis from O to P, r = O P →. The term position vector is used mostly in the fields of geometry, mechanics. Frequently this is used in two-dimensional or three-dimensional space, but can be generalized to Euclidean spaces in any number of dimensions. These different coordinates and corresponding basis vectors represent the position vector. More general curvilinear coordinates could be used instead, and are in contexts like continuum mechanics, 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 dimension of the position space is n. The coordinates of the vector r with respect to the 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. One parameter xi would describe a curved 1D path, two parameters xi describes a curved 2D surface, three xi describes a curved 3D volume of space, and so on. The linear span of a basis set B = equals the position space R, position vector fields are used to describe continuous and differentiable space curves, in which case the independent parameter needs not be time, but can be arc length of the curve. In the case of one dimension, the position has only one component and it could be, say, a vector in the x-direction, or the radial r-direction. Equivalent notations include, x ≡ x ≡ x, r ≡ r, s ≡ s ⋯ For a position vector r that is a function of time t and these derivatives have common utility in the study of kinematics, control theory, engineering and other sciences. Velocity v = d r d t where dr is a small displacement. 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. Such higher-order terms are required in order to represent the displacement function as a sum of an infinite sequence, enabling several analytical techniques in engineering. A displacement vector can be defined as the action of uniformly translating spatial points in a given direction over a given distance, thus the addition of displacement vectors expresses the composition of these displacement actions and scalar multiplication as scaling of the distance. With this in mind we may define a position vector of a point in space as the displacement vector mapping a given origin to that point. Note thus position vectors depend on a choice of origin for the space, affine space Six degrees of freedom Line element Parametric surface Keller, F. J, Gettys, W. E. et al
3.
Displacement (vector)
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A displacement is a vector that is 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 line from the initial position to the final position of the point. The velocity then is distinct from the speed which is the time rate of change of the distance traveled along a specific path. The velocity may be defined as the time rate of change of the position vector. For motion over an interval of time, the displacement divided by the length of the time interval defines the average velocity. In dealing with the motion of a 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, for a position vector s that is a function of time t, the derivatives can be computed with respect to t. These derivatives have common utility in the study of kinematics, control theory, vibration sensing and other sciences, by extension, the higher order derivatives can be computed in a similar fashion. Study of these higher order derivatives can improve approximations of the displacement function. Such higher-order terms are required in order to represent the displacement function as a sum of an infinite series, enabling several analytical techniques in engineering. The fourth order derivative is called jounce
4.
Distance
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Distance is a numerical description of how far apart objects are. In physics or everyday usage, distance may refer to a physical length, in most cases, distance from A to B is interchangeable with distance from B to A. In mathematics, a function or metric is a generalization of the concept of physical distance. A metric is a function that behaves according to a set of rules. The circumference of the wheel is 2π × radius, and assuming the radius to be 1, in engineering ω = 2πƒ is often used, where ƒ is the frequency. Chessboard distance, formalized as Chebyshev distance, is the number of moves a king must make on a chessboard to travel between two squares. Distance measures in cosmology are complicated by the expansion of the universe, the term distance is also used by analogy to measure non-physical entities in certain ways. In computer science, there is the notion of the distance between two strings. For example, the dog and dot, which vary by only one letter, are closer than dog and cat. In this way, many different types of distances can be calculated, such as for traversal of graphs, comparison of distributions and curves, distance cannot be negative, and distance travelled never decreases. Distance is a quantity or a magnitude, whereas displacement is a vector quantity with both magnitude and direction. Directed distance is a positive, zero, or negative scalar quantity, the distance covered by a vehicle, person, animal, or object along a curved path from a point A to a point B should be distinguished from the straight-line distance from A to B. For example, whatever the distance covered during a trip from A to B and back to A. In general the straight-line distance does not equal distance travelled, except for journeys in a straight line, directed distances are distances with a directional sense. They can be determined along straight lines and along curved lines, for instance, just labelling the two endpoints as A and B can indicate the sense, if the ordered sequence is assumed, which implies that A is the starting point. A displacement is a kind of directed distance defined in mechanics. A directed distance is called displacement when it is the distance along a line from A and B. This implies motion of the particle, the distance traveled by a particle must always be greater than or equal to its displacement, with equality occurring only when the particle moves along a straight path
5.
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, and 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 vector quantity, both magnitude and direction are needed to define it. The scalar absolute value of velocity is called speed, being a coherent derived unit whose quantity is measured in the SI system as metres per second or as the SI base unit of. For example,5 metres per second is a scalar, whereas 5 metres per second east is a vector, if there is a change in speed, direction or 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. For example, a car moving at a constant 20 kilometres per hour in a path has 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 and this is because the average velocity is calculated by only considering the displacement between the starting and the end points while the average speed considers only the total distance traveled. Velocity is defined as the rate of change of position with respect to time, average velocity can be calculated as, v ¯ = Δ x Δ t. The average velocity is less than or equal to the average speed of an object. This can be seen by realizing that while distance is always strictly increasing, from this derivative equation, in the one-dimensional case it can be seen that the area under a velocity vs. time is the displacement, x. In calculus terms, the integral of the velocity v is the displacement function x. In the figure, this corresponds to the area under the curve labeled s. Since the derivative of the position with respect to time gives the change in position divided by the change in time, although velocity is defined as the rate of change of position, it is often common to start with an expression for an objects acceleration. As seen by the three green tangent lines in the figure, an objects instantaneous acceleration at a point in time is the slope of the tangent to the curve of a v graph at that point. In other words, acceleration is defined as the derivative of velocity with respect to time, from there, we can obtain an expression for velocity as the area under an a acceleration vs. time graph
6.
Acceleration
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Acceleration, in physics, is the rate of change of velocity of an object with respect to time. An objects acceleration is the net result of any and all forces acting on the object, the SI unit for acceleration is metre per second squared. Accelerations are vector quantities and add according to the parallelogram law, as a vector, the calculated net force is equal to the product of the objects mass and its acceleration. For example, when a car starts from a standstill and travels in a line at increasing speeds. If the car turns, there is an acceleration toward the new direction, in this example, we can call the forward acceleration of the car a linear acceleration, which passengers in the car might experience as a force pushing them back into their seats. When changing direction, we 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 direction from the direction of the vehicle. 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 objects 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. The SI unit of acceleration is the metre per second squared, or metre per second per second, as the velocity in metres per second changes by the acceleration value, every second. An object moving in a circular motion—such as a satellite orbiting the Earth—is accelerating due to the change of direction of motion, in this case it is said to be undergoing centripetal acceleration. Proper acceleration, the acceleration of a relative to a free-fall condition, is measured by an instrument called an accelerometer. As speeds approach the speed of light, relativistic effects become increasingly large and these components are called the tangential acceleration and the normal or radial acceleration. Geometrical analysis of space curves, which explains tangent, normal and binormal, is described by the Frenet–Serret formulas. Uniform or constant acceleration is a type of motion in which the velocity of an object changes by an amount in every equal time period. A frequently cited example of uniform acceleration is that of an object in free fall in a gravitational field. The acceleration of a body in the absence of resistances to motion is dependent only on the gravitational field strength g
7.
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 dimension, along with the three spatial dimensions. Time has long been an important subject of study in religion, philosophy, and science, nevertheless, diverse fields such as business, industry, sports, the sciences, and 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 dimension independent of events, in which events occur in sequence. Isaac Newton subscribed to this realist view, and hence it is referred to as Newtonian time. This second view, in the tradition of Gottfried Leibniz and Immanuel Kant, holds that time is neither an event nor a thing, Time in physics is unambiguously operationally defined as what a clock reads. Time is one of the seven fundamental physical quantities in both the International System of Units and 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. The operational definition leaves aside the question there is something called time, apart from the counting activity just mentioned, that flows. Investigations of a single continuum called spacetime bring questions about space into questions about time, questions that have their roots in the works of early students of natural philosophy. Furthermore, it may be there is a subjective component to time. Temporal measurement has occupied scientists and technologists, and was a motivation in navigation. Periodic events and periodic motion have long served as standards for units of time, examples include the apparent motion of the sun across the sky, the phases of the moon, the swing of a pendulum, and the beat of a heart. Currently, the unit of time, the second, is defined by measuring the electronic transition frequency of caesium atoms. Time is also of significant social importance, having economic value as well as value, due to an awareness of the limited time in each day. In day-to-day life, the clock is consulted for periods less than a day whereas the calendar is consulted for periods longer than a day, increasingly, personal electronic devices display both calendars and clocks simultaneously. The number that marks the occurrence of an event as to hour or date is obtained by counting from a fiducial epoch—a central reference point. Artifacts from the Paleolithic suggest that the moon was used to time as early as 6,000 years ago. Lunar calendars were among the first to appear, either 12 or 13 lunar months, without intercalation to add days or months to some years, seasons quickly drift in a calendar based solely on twelve lunar months
8.
Speed
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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, the SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour. For air and marine travel the knot is commonly used, the fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in a vacuum c =299792458 metres per second. Matter cannot quite reach the speed of light, as this would require an amount of energy. In relativity physics, the concept of rapidity replaces the classical idea of speed, italian physicist Galileo Galilei is usually credited with being the first to measure speed by considering the distance covered and the time it takes. Galileo defined speed as the distance covered per unit of time, in equation form, this is v = d t, where v is speed, d is distance, and t is time. A cyclist who covers 30 metres in a time of 2 seconds, objects in motion often have variations in speed. If s is the length of the path travelled until time t, in the special case where the velocity is constant, this can be simplified to v = s / t. The average speed over a time interval is the total distance travelled divided by the time duration. Speed at some instant, or assumed constant during a short period of time, is called instantaneous speed. By looking at a speedometer, one can read the speed of a car at any instant. A car travelling at 50 km/h generally goes for less than one hour at a constant speed, if the vehicle continued at that speed for half an hour, it would cover half that distance. If it continued for one minute, it would cover about 833 m. Different from instantaneous speed, average speed is defined as the distance covered divided by the time interval. For example, if a distance of 80 kilometres is driven in 1 hour, likewise, if 320 kilometres are travelled in 4 hours, the average speed is also 80 kilometres per hour. When a distance in kilometres is divided by a time in hours, average speed does not describe the speed variations that may have taken place during shorter time intervals, and so average speed is often quite different from a value of instantaneous speed. If the average speed and the time of travel are known, using this equation for an average speed of 80 kilometres per hour on a 4-hour trip, the distance covered is found to be 320 kilometres. Linear speed is the distance travelled per unit of time, while speed is the linear speed of something moving along a circular path
9.
Frame of reference
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In physics, a frame of reference consists of an abstract coordinate system and the set of physical reference points that uniquely fix the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to define a reference frame. Using rectangular coordinates, a frame may be defined with a reference point at the origin. In Einsteinian relativity, reference frames are used to specify the relationship between an observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes observational frame of reference, a relativistic reference 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 possible 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 system is attached as a modifier. Sometimes the state of motion is emphasized, as in rotating frame of reference, sometimes the way it transforms to frames considered as related is emphasized as in Galilean frame of reference. Sometimes frames are distinguished by the scale of their observations, as in macroscopic and microscopic frames of reference, in this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a system may be employed for many purposes where the state of motion is not the primary concern. For example, a system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs generalized coordinates, normal modes or eigenvectors and it seems useful to divorce the various aspects of a reference frame for the discussion below. A coordinate system is a concept, amounting to a choice of language used to describe observations. Consequently, an observer in a frame of reference can choose to employ any coordinate system to describe observations made from that frame of reference. A change in the choice of coordinate system does not change an observers state of motion. This viewpoint can be found elsewhere as well, which is not to dispute that some coordinate systems may be a better choice for some observations than are others. Choice of what to measure and with what observational apparatus is a separate from the observers state of motion. D. Norton, The discussion is taken beyond simple space-time coordinate systems by Brading, extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity
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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 to change its velocity, force can also be described intuitively as a push or a pull. A force has both magnitude and direction, making it a vector quantity and it is measured in the SI unit of newtons and represented by the symbol F. The original form of Newtons second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. In an extended body, each part usually applies forces on the adjacent parts, such internal mechanical stresses cause no accelation of that body as the forces balance one another. Pressure, the distribution of small forces applied over an area of a body, is a simple type of stress that if unbalanced can cause the body to accelerate. Stress usually causes deformation of materials, or flow in fluids. In part this was due to an understanding of the sometimes non-obvious force of friction. A fundamental error was the belief that a force is required to maintain motion, most of the previous misunderstandings about motion and 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 three hundred years, the Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known, in order of decreasing strength, they are, strong, electromagnetic, weak, high-energy particle 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 as integral to the functioning of each of the simple machines. The mechanical advantage given by a machine allowed for less force to be used in exchange for that force acting over a greater distance for the same amount of work. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was famous for formulating a treatment of buoyant forces inherent in fluids. Aristotle provided a discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotles view, the sphere contained four elements that come to rest at different natural places therein. Aristotle believed that objects on Earth, those composed mostly of the elements earth and water, to be in their natural place on the ground. He distinguished between the tendency of objects to find their natural place, which led to natural motion, and unnatural or forced motion
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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 impulse, the product of force and time, Newtons 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 slowly, then it would have less momentum. Linear momentum is also a quantity, meaning that if a closed system is not affected by external forces. In classical mechanics, conservation of momentum is implied by Newtons laws. It also holds in special relativity and, with definitions, a linear momentum conservation law holds in electrodynamics, quantum mechanics, quantum field theory. It is ultimately an expression of one of the symmetries of space and time. 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 with time, momentum has a direction as well as magnitude. Quantities that have both a magnitude and 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, as well as their speeds. Below, the properties of momentum are described in one dimension. The vector equations are almost identical to the scalar equations, the momentum of a particle is traditionally represented by the letter p. It is the product of two quantities, the mass and velocity, p = m v, the units of momentum are the product of the units of mass and velocity. In SI units, if the mass is in kilograms and the velocity in meters per second then the momentum is in kilogram meters/second, in cgs units, if the mass is in grams and the velocity in centimeters per second, then the momentum is in gram centimeters/second. Being a vector, momentum has magnitude and direction, for example, a 1 kg model airplane, traveling due north at 1 m/s in straight and level flight, has a momentum of 1 kg m/s due north measured from the ground. The momentum of a system of particles is the sum of their momenta, if two particles have masses m1 and m2, and velocities v1 and v2, the total momentum is p = p 1 + p 2 = m 1 v 1 + m 2 v 2. If all the particles are moving, the center of mass will generally be moving as well, if the center of mass is moving at velocity vcm, the momentum is, p = m v cm. This is known as Eulers first law, if a force F is applied to a particle for a time interval Δt, the momentum of the particle changes by an amount Δ p = F Δ t
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Mass
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In physics, mass is a property of a physical body. It is the measure of a resistance to acceleration when a net force is applied. It also determines the strength of its gravitational attraction to other bodies. The basic SI unit of mass is the kilogram, Mass is not the same as weight, even though mass is often determined by measuring the objects weight using a spring scale, rather than comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity and 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 as the amount of matter in an object, however, at very high speeds, special relativity postulates that energy is an additional source of mass. Thus, any body having mass has an equivalent amount of energy. In addition, matter is a defined term in science. There are several distinct phenomena which can be used to measure mass, active gravitational mass measures the gravitational force exerted by an object. Passive gravitational mass measures the force exerted on an object in a known gravitational field. The mass of an object determines its acceleration in the presence of an applied force, according to Newtons second law of motion, if a body of fixed mass m is subjected to a single force F, its acceleration a is given by F/m. A bodys mass also determines the degree to which it generates or is affected by a gravitational field and this is sometimes referred to as gravitational mass. The standard International System of Units unit of mass is the kilogram, the kilogram is 1000 grams, first defined in 1795 as one cubic decimeter of water at the melting point of ice. Then in 1889, the kilogram was redefined as the mass of the prototype kilogram. As of January 2013, there are proposals for redefining the kilogram yet again. In this context, the mass has units of eV/c2, the electronvolt and its multiples, such as the MeV, are commonly used in particle physics. The atomic mass unit is 1/12 of the mass of a carbon-12 atom, the atomic mass unit is convenient for expressing the masses of atoms and molecules. Outside the SI system, other units of mass include, the slug is an Imperial unit of mass, the pound is a unit of both mass and force, used mainly in the United States
13.
Absolute space and time
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Absolute space and time is a concept in physics and philosophy about the properties of the universe. In physics, absolute space and time may be a preferred frame, a version of the concept of absolute space can be seen in Aristotelian physics. Westman writes that whiff of absolute space can be observed in Copernicus De revolutionibus orbium coelestium, according to Newton, absolute time exists independently of any perceiver and progresses at a consistent pace throughout the universe. Unlike relative time, Newton believed absolute time was imperceptible and could only be understood mathematically, according to Newton, humans are only capable of perceiving relative time, which is a measurement of perceivable objects in motion. From these movements, we infer the passage of time, absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the spaces, which our senses determine by its position to bodies. Absolute motion is the translation of a body from one place into another, and relative motion. These notions imply that absolute space and time do not depend upon physical events, thus, every object has an absolute state of motion relative to absolute space, so that an object must be either in a state of absolute rest, or moving at some absolute speed. Historically, there have been differing views on the concept of absolute space, gottfried Leibniz was of the opinion that space made no sense except as the relative location of bodies, and time made no sense except as the relative movement of bodies. A more recent form of objections was made by Ernst Mach. Machs principle proposes that mechanics is entirely about relative motion of bodies and, in particular, so, for example, a single particle in a universe with no other bodies would have zero mass. According to Mach, Newtons examples simply illustrate relative rotation of spheres, when, accordingly, we say that a body preserves unchanged its direction and velocity in space, our assertion is nothing more or less than an abbreviated reference to the entire universe. —Ernst Mach, as quoted by Ciufolini and Wheeler, Gravitation and Inertia, even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference has taken precedence, that is, absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames. Absolute space acts on objects by inducing their resistance to acceleration. Newton himself recognized the role of inertial frames, the motions of bodies included in a given space are the same among themselves, whether that space is at rest or moves uniformly forward in a straight line. As a practical matter, inertial frames often are taken as frames moving uniformly with respect to the fixed stars, see Inertial frame of reference for more discussion on this. In Einsteins theories, the ideas of time and space were superseded by the notion of spacetime in special relativity
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Yongsan Station
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Yongsan Station is a major railway station in Seoul, South Korea. It is located in Yongsan District, and adjoins the Yongsan Electronics Market, prior to 2004, all long-distance trains serving Seoul terminated at the nearby Seoul Station, but with the opening of the Korea Train Express, Yongsan Station took over some of Seouls services. On February 28,2012, ITX trains began service between this station and Chuncheon Station on the Gyeongchun Line, Yongsan Station is also served by metro rail on Line 1 and the Jungang Line on the Seoul Metropolitan Subway. In 2004, a cinema opened adjacent to the station. In August 2006, the station building was made into a large department store. The building now includes the station, subway station, the CGV cinema and several restaurants and shops. There is a bridge connecting IPark Mall and the Yongsan Electronics Market, on floors B-1 and B-2 there is a very large E-Mart store along with a food court and a Burger King restaurant. In the higher floors some of the include, Uno Chicago Grill, KFC, Lotteria, California Pizza Kitchen, Pizza Hut. You can also find Starbucks, Dunkin Donuts, and Baskin Robbins, in 2018 it will become a transfer station with the Shinbundang Line. Yongsan Station has six elevated platforms and one side platform serving 13 tracks. Transportation in South Korea Korail Korea Train Express Yongsan bombing
15.
Mechanics
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Mechanics is an area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment. The scientific discipline has its origins in Ancient Greece with the writings of Aristotle, during the early modern period, scientists such as Khayaam, Galileo, Kepler, and Newton, laid the foundation for what is now known as classical mechanics. It is a branch of physics that deals with particles that are either at rest or are moving with velocities significantly less than the speed of light. It can also be defined as a branch of science which deals with the motion of, historically, classical mechanics came first, while quantum mechanics is a comparatively recent invention. Classical mechanics originated with Isaac Newtons laws of motion in Philosophiæ Naturalis Principia Mathematica, both are commonly held to constitute the most certain knowledge that exists about physical nature. Classical mechanics has especially often been viewed as a model for other so-called exact sciences, essential in this respect is the relentless use of mathematics in theories, as well as the decisive role played by experiment in generating and testing them. Quantum mechanics is of a scope, as it encompasses classical mechanics as a sub-discipline which applies under certain restricted circumstances. According to the principle, there is no contradiction or conflict between the two subjects, each simply pertains to specific situations. The correspondence principle states that the behavior of systems described by quantum theories reproduces classical physics in the limit of quantum numbers. Quantum mechanics has superseded classical mechanics at the level and is indispensable for the explanation and prediction of processes at the molecular, atomic. However, for macroscopic processes classical mechanics is able to solve problems which are difficult in quantum mechanics and hence remains useful. Modern descriptions of such behavior begin with a definition of such quantities as displacement, time, velocity, acceleration, mass. Until about 400 years ago, however, motion was explained from a different point of view. He showed that the speed of falling objects increases steadily during the time of their fall and this acceleration is the same for heavy objects as for light ones, provided air friction is discounted. The English mathematician and physicist Isaac Newton improved this analysis by defining force and mass, for objects traveling at speeds close to the speed of light, Newton’s laws were superseded by Albert Einstein’s theory of relativity. For atomic and subatomic particles, Newton’s laws were superseded by quantum theory, for everyday phenomena, however, Newton’s three laws of motion remain the cornerstone of dynamics, which is the study of what causes motion. In analogy to the distinction between quantum and classical mechanics, Einsteins general and special theories of relativity have expanded the scope of Newton, the differences between relativistic and Newtonian mechanics become significant and even dominant as the velocity of a massive body approaches the speed of light. Relativistic corrections are also needed for quantum mechanics, although general relativity has not been integrated, the two theories remain incompatible, a hurdle which must be overcome in developing a theory of everything
16.
Projectile
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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, mathematical equations of motion are used to analyze projectile trajectory. Blowguns and 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 electromagnetic fields to provide a constant acceleration along the length of the device. Some projectiles provide propulsion during flight by means of an 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 rocket engine. An explosion, whether or not by a weapon, causes the debris to act as high velocity projectiles. An explosive weapon, or device may also be designed to produce high velocity projectiles by the break-up of its casing. Many projectiles, e. g. shells, may carry a charge or another chemical or biological substance. Aside from explosive payload, a projectile can be designed to cause damage, e. g. fire. Typical kinetic energy weapons are blunt projectiles such as rocks and round shots, pointed ones such as arrows, among projectiles that do not contain explosives are those launched from railguns, coilguns, and mass drivers, as well as kinetic energy penetrators. Other types of weapons are accelerated over time by a rocket engine. In either case, it is the energy of the projectile that destroys its target. Some kinetic weapons for targeting objects in spaceflight are anti-satellite weapons, since in order to reach an object in orbit it is necessary to attain an extremely high velocity, their released kinetic energy alone is enough to destroy their target, explosives are not necessary. For example, the energy of TNT is 4.6 MJ/kg, and this saves costly weight and there is no detonation to be precisely timed. This method, however, requires direct contact with the target, some hit-to-kill warheads are additionally equipped with an explosive directional warhead to enhance the kill probability. With regard to weapons, the Arrow missile and MIM-104 Patriot PAC-2 have explosives, while the Kinetic Energy Interceptor, Lightweight Exo-Atmospheric Projectile. A kinetic projectile can also be dropped from aircraft and this is applied by replacing the explosives of a regular bomb with a non-explosive material, for a precision hit with less collateral damage
17.
Planet
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The term planet is ancient, with ties to history, astrology, science, mythology, and religion. Several planets in the Solar System can be seen with the naked eye and these were regarded by many early cultures as divine, or as emissaries of deities. As scientific knowledge advanced, human perception of the planets changed, in 2006, the International Astronomical Union officially adopted a resolution defining planets within the Solar System. This definition is controversial because it excludes many objects of mass based on where or what they orbit. The planets were thought by Ptolemy to orbit Earth in deferent, at about the same time, by careful analysis of pre-telescopic observation data collected by Tycho Brahe, Johannes Kepler found the planets orbits were not circular but elliptical. As observational tools improved, astronomers saw that, like Earth, the planets rotated around tilted axes, and some shared such features as ice caps and seasons. Since the dawn of the Space Age, close observation by space probes has found that Earth and the planets share characteristics such as volcanism, hurricanes, tectonics. Planets are generally divided into two types, large low-density giant planets, and smaller rocky terrestrials. Under IAU definitions, there are eight planets in the Solar System, in order of increasing distance from the Sun, they are the four terrestrials, Mercury, Venus, Earth, and Mars, then the four giant planets, Jupiter, Saturn, Uranus, and Neptune. Six of the planets are orbited by one or more natural satellites, several thousands of planets around other stars have been discovered in the Milky Way. e. in the habitable zone. On December 20,2011, the Kepler Space Telescope team reported the discovery of the first Earth-sized extrasolar planets, Kepler-20e and Kepler-20f, orbiting a Sun-like star, Kepler-20. A2012 study, analyzing gravitational microlensing data, estimates an average of at least 1.6 bound planets for every star in the Milky Way, around one in five Sun-like stars is thought to have an Earth-sized planet in its habitable zone. The idea of planets has evolved over its history, from the lights of antiquity to the earthly objects of the scientific age. The concept has expanded to include not only in the Solar System. The ambiguities inherent in defining planets have led to much scientific controversy, the five classical planets, being visible to the naked eye, have been known since ancient times and have had a significant impact on mythology, religious cosmology, and ancient astronomy. In ancient times, astronomers noted how certain lights moved across the sky, as opposed to the fixed stars, ancient Greeks called these lights πλάνητες ἀστέρες or simply πλανῆται, from which todays word planet was derived. In ancient Greece, China, Babylon, and indeed all pre-modern civilizations, it was almost universally believed that Earth was the center of the Universe and that all the planets circled Earth. The first civilization known to have a theory of the planets were the Babylonians
18.
Cell (biology)
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The cell is the basic structural, functional, and biological unit of all known living organisms. A cell is the smallest unit of life that can replicate independently, the study of cells is called cell biology. Cells consist of cytoplasm enclosed within a membrane, which contains many such as proteins. Organisms can be classified as unicellular or multicellular, while the number of cells in plants and animals varies from species to species, humans contain more than 10 trillion cells. Most plant and animal cells are only under a microscope. The cell was discovered by Robert Hooke in 1665, who named the unit for its resemblance to cells inhabited by Christian monks in a monastery. Cells emerged on Earth at least 3.5 billion years ago, Cells are of two types, eukaryotic, which contain a nucleus, and prokaryotic, which do not. Prokaryotes are single-celled organisms, while eukaryotes can be either single-celled or multicellular, prokaryotic cells were the first form of life on Earth, characterised by having vital biological processes including cell signaling and being self-sustaining. They are simpler and smaller than eukaryotic cells, and lack membrane-bound organelles such as the nucleus, prokaryotes include two of the domains of life, bacteria and archaea. The DNA of a prokaryotic cell consists of a chromosome that is in direct contact with the cytoplasm. The nuclear region in the cytoplasm is called the nucleoid, most prokaryotes are the smallest of all organisms ranging from 0.5 to 2.0 µm in diameter. Though most prokaryotes have both a cell membrane and a wall, there are exceptions such as Mycoplasma and Thermoplasma which only possess the cell membrane layer. The envelope gives rigidity to the cell and separates the interior of the cell from its environment, the cell wall consists of peptidoglycan in bacteria, and acts as an additional barrier against exterior forces. It also prevents the cell from expanding and bursting from osmotic pressure due to a hypotonic environment, some eukaryotic cells also have a cell wall. Inside the cell is the region that contains the genome, ribosomes. The genetic material is found in the cytoplasm. Prokaryotes can carry extrachromosomal DNA elements called plasmids, which are usually circular, linear bacterial plasmids have been identified in several species of spirochete bacteria, including members of the genus Borrelia notably Borrelia burgdorferi, which causes Lyme disease. Though not forming a nucleus, the DNA is condensed in a nucleoid, plasmids encode additional genes, such as antibiotic resistance genes
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Human
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Modern humans are the only extant members of Hominina tribe, a branch of the tribe Hominini belonging to the family of great apes. Several of these hominins used fire, occupied much of Eurasia and they began to exhibit evidence of behavioral modernity around 50,000 years ago. In several waves of migration, anatomically modern humans ventured out of Africa, the spread of humans and their large and increasing population has had a profound impact on large areas of the environment and millions of native species worldwide. Humans are uniquely adept at utilizing systems of communication for self-expression and the exchange of ideas. Humans create complex structures composed of many cooperating and competing groups, from families. Social interactions between humans have established a wide variety of values, social norms, and rituals. These human societies subsequently expanded in size, establishing various forms of government, religion, today the global human population is estimated by the United Nations to be near 7.5 billion. In common usage, the word generally refers to the only extant species of the genus Homo—anatomically and behaviorally modern Homo sapiens. In scientific terms, the meanings of hominid and hominin have changed during the recent decades with advances in the discovery, there is also a distinction between anatomically modern humans and Archaic Homo sapiens, the earliest fossil members of the species. The English adjective human is a Middle English loanword from Old French humain, ultimately from Latin hūmānus, the words use as a noun dates to the 16th century. The native English term man can refer to the species generally, the species binomial Homo sapiens was coined by Carl Linnaeus in his 18th century work Systema Naturae. The generic name Homo is a learned 18th century derivation from Latin homō man, the species-name sapiens means wise or sapient. Note that the Latin word homo refers to humans of either gender, the genus Homo evolved and diverged from other hominins in Africa, after the human clade split from the chimpanzee lineage of the hominids branch of the primates. The closest living relatives of humans are chimpanzees and gorillas, with the sequencing of both the human and chimpanzee genome, current estimates of similarity between human and chimpanzee DNA sequences range between 95% and 99%. The gibbons and orangutans were the first groups to split from the leading to the humans. The splitting date between human and chimpanzee lineages is placed around 4–8 million years ago during the late Miocene epoch, during this split, chromosome 2 was formed from two other chromosomes, leaving humans with only 23 pairs of chromosomes, compared to 24 for the other apes. There is little evidence for the divergence of the gorilla, chimpanzee. Each of these species has been argued to be an ancestor of later hominins
20.
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 oldest and largest subjects in science, engineering and technology. Classical mechanics describes the motion of objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars. Within classical mechanics are fields of study that describe the behavior of solids, liquids and gases, Classical mechanics also provides extremely accurate results as long as the domain of study is restricted to large objects and the speeds involved do not approach the speed of light. When both quantum and classical mechanics cannot apply, such as at the level with high speeds. Since these aspects of physics were developed long before the emergence of quantum physics and relativity, however, a number of modern sources do include relativistic mechanics, which in their view represents classical mechanics in its most developed and accurate form. Later, more abstract and general methods were developed, leading to reformulations of classical mechanics known as Lagrangian mechanics and these advances were largely made in the 18th and 19th centuries, and they extend substantially beyond Newtons work, particularly through their use of analytical mechanics. The following introduces the concepts of classical mechanics. For simplicity, it often models real-world objects as point particles, the motion of a point particle is characterized by a small number of parameters, its position, mass, and the forces applied to it. Each of these parameters is discussed in turn, in reality, the kind of objects that classical mechanics can describe always have a non-zero size. Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the degrees of freedom. However, the results for point particles can be used to such objects by treating them as composite objects. The center of mass of a composite object behaves like a point particle, Classical mechanics uses common-sense notions of how matter and forces exist and interact. It assumes that matter and energy have definite, knowable attributes such as where an object is in space, non-relativistic mechanics also assumes that forces act instantaneously. The position of a point particle is defined with respect to a fixed reference point in space called the origin O, in space. A simple coordinate system might describe the position of a point P by means of a designated as r. In general, the point particle need not be stationary relative to O, such that r is a function of t, the time
21.
Atom
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An atom is the smallest constituent unit of ordinary matter that has the properties of a chemical element. Every solid, liquid, gas, and plasma is composed of neutral or ionized atoms, Atoms are very small, typical sizes are around 100 picometers. Atoms are small enough that attempting to predict their behavior using classical physics - as if they were billiard balls, through the development of physics, atomic models have incorporated quantum principles to better explain and predict the behavior. Every atom is composed of a nucleus and one or more bound to the nucleus. The nucleus is made of one or more protons and typically a number of neutrons. Protons and neutrons are called nucleons, more than 99. 94% of an atoms mass is in the nucleus. The protons have an electric charge, the electrons have a negative electric charge. If the number of protons and electrons are equal, that atom is electrically neutral, if an atom has more or fewer electrons than protons, then it has an overall negative or positive charge, respectively, and it is called an ion. The electrons of an atom are attracted to the protons in a nucleus by this electromagnetic force. The number of protons in the nucleus defines to what chemical element the atom belongs, for example, the number of neutrons defines the isotope of the element. The number of influences the magnetic properties of an atom. Atoms can attach to one or more other atoms by chemical bonds to form compounds such as molecules. The ability of atoms to associate and dissociate is responsible for most of the changes observed in nature. The idea that matter is made up of units is a very old idea, appearing in many ancient cultures such as Greece. The word atom was coined by ancient Greek philosophers, however, these ideas were founded in philosophical and theological reasoning rather than evidence and experimentation. As a result, their views on what look like. They also could not convince everybody, so atomism was but one of a number of competing theories on the nature of matter. It was not until the 19th century that the idea was embraced and refined by scientists, in the early 1800s, John Dalton used the concept of atoms to explain why elements always react in ratios of small whole numbers
22.
Subatomic particle
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In the physical sciences, subatomic particles are particles much smaller than atoms. There are two types of particles, elementary particles, which according to current theories are not made of other particles. Particle physics and nuclear physics study these particles and how they interact, in particle physics, the concept of a particle is one of several concepts inherited from classical physics. But it also reflects the understanding that at the quantum scale matter. The idea of a particle underwent serious rethinking when experiments showed that light could behave like a stream of particles as well as exhibit wave-like properties and this led to the new concept of wave–particle duality to reflect that quantum-scale particles behave like both particles and waves. Another new concept, the uncertainty principle, states that some of their properties taken together, such as their simultaneous position and momentum, in more recent times, wave–particle duality has been shown to apply not only to photons but to increasingly massive particles as well. Interactions of particles in the framework of field theory are understood as creation and annihilation of quanta of corresponding fundamental interactions. This blends particle physics with field theory, any subatomic particle, like any particle in the 3-dimensional space that obeys laws of quantum mechanics, can be either a boson or a fermion. Various extensions of the Standard Model predict the existence of a graviton particle. Composite subatomic particles are bound states of two or more elementary particles, for example, a proton is made of two up quarks and one down quark, while the atomic nucleus of helium-4 is composed of two protons and two neutrons. The neutron is made of two quarks and one up quark. Composite particles include all hadrons, these include baryons and mesons, in special relativity, the energy of a particle at rest equals its mass times the speed of light squared, E = mc2. That is, mass can be expressed in terms of energy, if a particle has a frame of reference where it lies at rest, then it has a positive rest mass and is referred to as massive. Baryons tend to have greater mass than mesons, which in turn tend to be heavier than leptons and it is also certain that any particle with an electric charge is massive. These include the photon and gluon, although the latter cannot be isolated, through the work of Albert Einstein, Satyendra Nath Bose, Louis de Broglie, and many others, current scientific theory holds that all particles also have a wave nature. This has been verified not only for elementary particles but also for compound particles like atoms, interactions between particles have been scrutinized for many centuries, and a few simple laws underpin how particles behave in collisions and interactions. These are the basics of Newtonian mechanics, a series of statements and equations in Philosophiae Naturalis Principia Mathematica. The negatively charged electron has an equal to 1⁄1837 or 1836 of that of a hydrogen atom
23.
Quantum mechanics
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Quantum mechanics, including quantum field theory, is a branch of physics which is the fundamental theory of nature at small scales and low energies of atoms and subatomic particles. Classical physics, the physics existing before quantum mechanics, derives from quantum mechanics as an approximation valid only at large scales, early quantum theory was profoundly reconceived in the mid-1920s. The reconceived theory is formulated in various specially developed mathematical formalisms, in one of them, a mathematical function, the wave function, provides information about the probability amplitude of position, momentum, and other physical properties of a particle. In 1803, Thomas Young, an English polymath, performed the famous experiment that he later described in a paper titled On the nature of light. This experiment played a role in the general acceptance of the wave theory of light. In 1838, Michael Faraday discovered cathode rays, Plancks hypothesis that energy is radiated and absorbed in discrete quanta precisely matched the observed patterns of black-body radiation. In 1896, Wilhelm Wien empirically determined a distribution law of black-body radiation, ludwig Boltzmann independently arrived at this result by considerations of Maxwells equations. However, it was only at high frequencies and underestimated the radiance at low frequencies. Later, Planck corrected this model using Boltzmanns statistical interpretation of thermodynamics and proposed what is now called Plancks law, following Max Plancks solution in 1900 to the black-body radiation problem, Albert Einstein offered a quantum-based theory to explain the photoelectric effect. Among the first to study quantum phenomena in nature were Arthur Compton, C. V. Raman, robert Andrews Millikan studied the photoelectric effect experimentally, and Albert Einstein developed a theory for it. In 1913, Peter Debye extended Niels Bohrs theory of structure, introducing elliptical orbits. This phase is known as old quantum theory, according to Planck, each energy element is proportional to its frequency, E = h ν, where h is Plancks constant. Planck cautiously insisted that this was simply an aspect of the processes of absorption and emission of radiation and had nothing to do with the reality of the radiation itself. In fact, he considered his quantum hypothesis a mathematical trick to get the right rather than a sizable discovery. He won the 1921 Nobel Prize in Physics for this work, lower energy/frequency means increased time and vice versa, photons of differing frequencies all deliver the same amount of action, but do so in varying time intervals. High frequency waves are damaging to human tissue because they deliver their action packets concentrated in time, the Copenhagen interpretation of Niels Bohr became widely accepted. In the mid-1920s, developments in mechanics led to its becoming the standard formulation for atomic physics. In the summer of 1925, Bohr and Heisenberg published results that closed the old quantum theory, out of deference to their particle-like behavior in certain processes and measurements, light quanta came to be called photons
24.
Inertial frame of reference
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In classical physics and special relativity, an inertial frame of reference is a frame of reference that describes time and space homogeneously, isotropically, and in a time-independent manner. The physics of a system in an inertial frame have no causes external to the system, all inertial frames are in a state of constant, rectilinear motion with respect to one another, an accelerometer moving with any of them would detect zero acceleration. Measurements in one frame can be converted to measurements in another by a simple transformation. In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, systems in non-inertial frames in general relativity dont have external causes because of the principle of geodesic motion. Physical laws take the form in all inertial frames. For example, a ball dropped towards the ground does not go 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—other bodies, observers and 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, however, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, 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, Newtons first law, the law of inertia, is satisfied, Any free motion has a constant magnitude, the force F is the vector sum of all real forces on the particle, such as electromagnetic, gravitational, nuclear and so forth. The extra terms in the force F′ are the forces for this frame. The first extra term is the Coriolis force, the second the centrifugal force, also, fictitious forces do not drop off with distance. For example, the force that appears to emanate from the axis of rotation in a rotating frame increases with distance from the axis. All observers agree on the forces, F, only non-inertial observers need fictitious forces. The laws of physics in the frame are simpler because unnecessary forces are not present. In Newtons time the stars were invoked as a reference frame
25.
Net force
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In physics, net force is the overall force acting on an object. In order to calculate the net force, the body is isolated and it is always possible to determine the torque associated with a point of application of a net force so that it maintains the movement of the object under the original system of forces. With its associated torque, the net force becomes the resultant force and has the effect on the rotational motion of the object as all actual forces taken together. It is possible for a system of forces to define a torque-free resultant force, in this case, the net force when applied at the proper line of action has the same effect on the body as all of the forces at their points of application. It is not always possible to find a torque-free resultant force, the sum of forces acting on a particle is called the total force or the net force. The net force is a force that replaces the effect of the original forces on the particles motion. It gives the particle the same acceleration as all actual forces together as described by the Newtons second law of motion. Force is a quantity, which means that it has a magnitude and a direction. Graphically, a force is represented as line segment from its point of application A to a point B which defines its direction, the length of the segment AB represents the magnitude of the force. Vector calculus was developed in the late 1800s and early 1900s, the parallelogram rule used for the addition of forces, however, dates from antiquity and is noted explicitly by Galileo and Newton. The diagram shows the addition of the forces F →1 and F →2, the sum F → of the two forces is drawn as the diagonal of a parallelogram defined by the two forces. Forces applied to a body can have different points of application. Forces are bound vectors and can be added if they are applied at the same point. The net force on a body applied at a point with the appropriate torque is known as the resultant force. A force is known as a vector which means it has a direction and magnitude. A convenient way to define a force is by a segment from a point A to a point B. If we denote the coordinates of points as A= and B=. The length of the vector B-A defines the magnitude of F and is given by | F | =2 +2 +2, the sum of two forces F1 and F2 applied at A can be computed from the sum of the segments that define them
26.
Euclidean vector
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In mathematics, physics, and engineering, a Euclidean vector is a geometric object that has magnitude and direction. Vectors can be added to other vectors according to vector algebra, a Euclidean vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by A B →. A vector is what is needed to carry the point A to the point B and it was first used by 18th century astronomers investigating planet rotation around the Sun. The magnitude of the vector is the distance between the two points and the direction refers to the direction of displacement from A to B. These operations and associated laws qualify Euclidean vectors as an example of the more generalized concept of vectors defined simply as elements of a vector space. Vectors play an important role in physics, the velocity and acceleration of a moving object, many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances, their magnitude and direction can still be represented by the length, the mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the system include pseudovectors and tensors. The concept of vector, as we know it today, evolved gradually over a period of more than 200 years, about a dozen people made significant contributions. Giusto Bellavitis abstracted the basic idea in 1835 when he established the concept of equipollence, working in a Euclidean plane, he made equipollent any pair of line segments of the same length and orientation. Essentially he realized an equivalence relation on the pairs of points in the plane, the term vector was introduced by William Rowan Hamilton as part of a quaternion, which is a sum q = s + v of a Real number s and a 3-dimensional vector. Like Bellavitis, Hamilton viewed vectors as representative of classes of equipollent directed segments, grassmanns work was largely neglected until the 1870s. Peter Guthrie Tait carried the standard after Hamilton. His 1867 Elementary Treatise of Quaternions included extensive treatment of the nabla or del operator ∇, in 1878 Elements of Dynamic was published by William Kingdon Clifford. Clifford simplified the quaternion study by isolating the dot product and cross product of two vectors from the complete quaternion product and this approach made vector calculations available to engineers and others working in three dimensions and skeptical of the fourth. Josiah Willard Gibbs, who was exposed to quaternions through James Clerk Maxwells Treatise on Electricity and Magnetism, the first half of Gibbss Elements of Vector Analysis, published in 1881, presents what is essentially the modern system of vector analysis. In 1901 Edwin Bidwell Wilson published Vector Analysis, adapted from Gibbs lectures, in physics and engineering, a vector is typically regarded as a geometric entity characterized by a magnitude and a direction. It is formally defined as a line segment, or arrow
27.
Newton's laws of motion
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Newtons 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, and its motion in response to those forces. More precisely, the first law defines the force qualitatively, the second law offers a measure of the force. These three laws have been expressed in different ways, over nearly three centuries, and can be summarised as follows. The three laws of motion were first compiled by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica, Newton used them to explain and investigate the motion of many physical objects and systems. For example, in the volume of the text, Newton showed that these laws of motion, combined with his law of universal gravitation. Newtons laws are applied to objects which are idealised as single point masses, in the sense that the size and this can be done when the object is small compared to the distances involved in its analysis, or the deformation and rotation of the body are of no importance. 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, Newtons laws of motion are not adequate to characterise the motion of rigid bodies and deformable bodies. Leonhard Euler in 1750 introduced a generalisation of Newtons laws of motion for rigid bodies called Eulers laws of motion, if a body is represented as an assemblage of discrete particles, each governed by Newtons laws of motion, then Eulers laws can be derived from Newtons laws. Eulers laws can, however, be taken as axioms describing the laws of motion for extended bodies, Newtons 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 Newtons death. In the given mass, acceleration, momentum, and force are assumed to be externally defined quantities. This is the most common, but not the interpretation of the way one can consider the laws to be a definition of these quantities. Newtonian mechanics has been superseded by special relativity, but it is useful as an approximation when the speeds involved are much slower than the speed of light. The first law states that if the net force is zero, the first law can be stated mathematically when the mass is a non-zero constant, as, ∑ F =0 ⇔ d v d t =0. Consequently, An object that is at rest will stay at rest unless a force acts upon it, an object that is in motion will not change its velocity unless a force acts upon it. This is known as uniform motion, an object continues to do whatever it happens to be doing unless a force is exerted upon it. If it is at rest, it continues in a state of rest, if an object is moving, it continues to move without turning or changing its speed
28.
Continuum mechanics
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Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics and the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century, research in the area continues till 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 solids and fluids which are independent of any particular coordinate system in which they are observed. These physical properties are 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, liquids and gases, are composed of molecules separated by space. On a microscopic scale, materials have cracks and discontinuities, a continuum is a body that can be continually sub-divided into infinitesimal elements with properties being those of the bulk material. More specifically, the continuum hypothesis/assumption hinges on the concepts of an elementary volume. This condition provides a link between an experimentalists and a viewpoint on constitutive equations as well as a way of spatial and statistical averaging of the microstructure. The latter then provide a basis for stochastic 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 car traffic on a highway---with just one lane for simplicity. Somewhat surprisingly, and in a tribute to its effectiveness, continuum mechanics effectively models the movement of cars via a differential equation for the density of cars. The familiarity of this situation empowers us to understand a little of the continuum-discrete dichotomy underlying continuum modelling in general. To start modelling define that, x measure distance along the highway, t is time, ρ is the density of cars on the highway, cars do not appear and disappear. Consider any group of cars, from the car at the back of the group located at x = a to the particular car at the front located at x = b. The total number of cars in this group N = ∫ a b ρ d x, since cars are conserved d N / d t =0. The only way an integral can be zero for all intervals is if the integrand is zero for all x, consequently, conservation derives the first order nonlinear conservation PDE ∂ ρ ∂ t + ∂ ∂ x =0 for all positions on the highway. This conservation PDE applies not only to car traffic but also to fluids, solids, crowds, animals, plants, bushfires, financial traders and this PDE is one equation with two unknowns, so another equation is needed to form a well posed problem
29.
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, in mechanical engineering, robotics, and biomechanics kinematics is used to describe the motion of systems composed of joined parts such as an engine, a robotic arm or the human skeleton. Kinematic analysis is the process of measuring the quantities used to describe motion. In addition, kinematics applies geometry to the study of the mechanical advantage of a mechanical system or mechanism. The term kinematic is the English version of A. M, ampères cinématique, which he constructed from the Greek κίνημα kinema, itself derived from κινεῖν kinein. Kinematic and cinématique are related to the French word cinéma, particle kinematics is the study of the trajectory of a particle. The position of a particle is defined to be the vector from the origin of a coordinate frame to the particle. If the tower is 50 m high, then the vector to the top of the tower is r=. In the most general case, a coordinate system is used to define the position of a particle. However, if the particle is constrained to move in a surface, all observations in physics are incomplete without those observations being described with respect to a reference frame. The position vector of a particle is a vector drawn from the origin of the frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin, the magnitude of the position vector |P| gives the distance between the point P and the origin. | P | = x P2 + y P2 + z P2, the direction cosines of the position vector provide a quantitative measure of direction. It is important to note that the vector of a particle isnt unique. The position vector of a particle is different relative to different frames of reference. The velocity of a particle is a quantity that describes the direction of motion. More mathematically, the rate of change of the vector of a point
30.
Statics
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When in static equilibrium, the acceleration of the system is zero and the system is either at rest, or its center of mass moves at constant velocity. The application of Newtons 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 acting on the system, m is the mass of the system. The summation of forces will give the direction and the magnitude of the acceleration will be proportional to the mass. The assumption of static equilibrium of a =0 leads to, 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 leads to. The summation of moments, one of which might be unknown and these two equations together, can be applied to solve for as many as two loads acting on the system. From Newtons first law, this implies that the net force, the net forces equaling zero is known as the first condition for equilibrium, and the net torque equaling zero is known as the second condition for equilibrium. A scalar is a quantity which only has a magnitude, such as mass or temperature, a vector has a magnitude and a direction. There are several notations to identify a vector, including, A bold faced character V An underlined character V A character with an arrow over it V →, vectors are added using the parallelogram law or the triangle law. Vectors contain components in orthogonal bases, unit vectors i, j, and k are, by convention, along the x, y, and z axes, respectively. Force is the action of one body on another, a force is either a push or a pull. A force tends to move a body in the direction of its action, the action of a force is characterized by its magnitude, by the direction of its action, and by its point of application. Thus, force is a quantity, because its effect depends on the direction as well as on the magnitude of the action. Forces are classified as either contact or body forces, a contact force is produced by direct physical contact, an example is the force exerted on a body by a supporting surface. A body force is generated by virtue of the position of a body within a field such as a gravitational, electric. An example of a force is the weight of a body in the Earths gravitational field. In addition to the tendency to move a body in the direction of its application, the axis may be any line which neither intersects nor is parallel to the line of action of the force
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Angular momentum
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In physics, angular momentum is the rotational analog of linear momentum. It is an important quantity in physics because it is a conserved quantity – the angular momentum of a system remains constant unless acted on by an external torque. The definition of momentum for a point particle is a pseudovector r×p. This definition can be applied to each point in continua like solids or fluids, unlike momentum, angular momentum does depend on where the origin is chosen, since the particles 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. However, while ω always points in the direction of the rotation axis, 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, inertial systems, reaction wheels, flying discs or Frisbees. In general, conservation does limit the motion of a system. 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 bodys rotational inertia and rotational velocity about a particular axis. Angular momentum can be considered an analog of linear momentum. Thus, where momentum is proportional to mass m and linear speed v, p = m v, angular momentum is proportional to moment of inertia I. Unlike mass, which only on amount of matter, moment of inertia is also dependent on the position of the axis of rotation. Unlike linear speed, which occurs in a line, angular speed occurs about a center of rotation. Therefore, strictly speaking, L should be referred to as the angular momentum relative to that center and this simple analysis can also apply to non-circular motion if only the component of the motion which is perpendicular to the radius vector is considered. In that case, L = r m v ⊥, where v ⊥ = v sin θ is the component of the motion. It is this definition, × to which the moment of momentum refers
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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 and 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, 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, definition A couple is a pair of forces, equal in magnitude, oppositely directed, and 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 and this is called a simple couple. The forces have an effect or moment called a torque about an axis which is normal to the plane of the forces. The SI unit for the torque of the couple is newton metre. When d is taken as a vector between the points of action of the forces, then the couple is the product of d and F, i. e. τ = | d × F |. The moment of a force is defined with respect to a certain point P, and in general when P is changed. However, the moment of a couple is independent of the reference point P, in other words, a torque vector, unlike any other moment vector, is a free vector. The proof of claim is as follows, Suppose there are a set of force vectors F1, F2, etc. that form a couple, with position vectors r1, r2. The moment about P is M = r 1 × F1 + r 2 × F2 + ⋯ Now we pick a new reference point P that differs from P by the vector r. The new moment is M ′ = × F1 + × F2 + ⋯ Now the distributive property of the cross product implies M ′ = + r ×, however, the definition of a force couple means that F1 + F2 + ⋯ =0. Therefore, M ′ = r 1 × F1 + r 2 × F2 + ⋯ = M This proves that the moment is independent of reference point, which is proof that a couple is a free vector. A force F applied to a body at a distance d from the center of mass has the same effect as the same force applied directly to the center of mass. The couple produces an acceleration of the rigid body at right angles to the plane of the couple. The force at the center of mass accelerates the body in the direction of the force without change in orientation, conversely, a couple and a force in the plane of the couple can be replaced by a single force, appropriately located
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D'Alembert's principle
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DAlemberts principle, also known as the Lagrange–dAlembert principle, is a statement of the fundamental classical laws of motion. It is named after its discoverer, the French physicist and mathematician Jean le Rond dAlembert and it is the dynamic analogue to the principle of virtual work for applied forces in a static system and in fact is more general than Hamiltons principle, avoiding restriction to holonomic systems. A holonomic constraint depends only on the coordinates and time and it does not depend on the velocities. The principle does not apply for irreversible displacements, such as sliding friction, DAlemberts 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 and it is equivalent to the somewhat more cumbersome Gausss principle of least constraint. The general statement of dAlemberts principle mentions the time derivatives of the momenta of the system. The momentum of the mass is the product of its mass and velocity, p i = m i v i. In many applications, the masses are constant and this reduces to p i ˙ = m i v ˙ i = m i a i. However, some applications involve changing masses and in those cases both terms m ˙ i v i and m i v ˙ i have to remain present, to date, nobody has shown that DAlemberts principle is equivalent to Newtons Second Law. This is true only for very special cases e. g. rigid body constraints. However, a solution to this problem does exist. Consider Newtons law for a system of particles, i, if arbitrary 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 and this leads to the formulation of dAlemberts principle, which states that the difference of applied forces and inertial forces for a dynamic system does no virtual work. There is also a principle for static systems called the principle of virtual work for applied forces. DAlembert showed that one can transform an accelerating rigid body into an equivalent static system by adding the so-called inertial force, the inertial force must act through the center of mass and the inertial torque can act anywhere. The system can then be analyzed exactly as a static system subjected to this force and moment. The advantage is that, in the equivalent static system one can take moments about any point and this often leads to simpler calculations because any force can be eliminated from the moment equations by choosing the appropriate point about which to apply the moment equation. Even in the course of Fundamentals of Dynamics and Kinematics of machines, in textbooks of engineering dynamics this is sometimes referred to as dAlemberts principle
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Energy
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In physics, energy is the property that must be transferred to an object in order to perform work on – or to heat – the object, and can be converted in form, but not created or destroyed. The SI unit of energy is the joule, which is the transferred to an object by the mechanical work of moving it a distance of 1 metre against a force of 1 newton. Mass and energy are closely related, for example, 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 humans get from food. Civilisation gets the energy it needs from energy resources such as fuels, nuclear fuel. The processes of Earths climate and ecosystem are driven by the radiant energy Earth receives from the sun, the total energy of a system can be subdivided and classified in various ways. It may also be convenient to distinguish gravitational energy, thermal energy, several types of energy, electric energy. Many of these overlap, for instance, thermal energy usually consists partly of kinetic. Some types of energy are a mix of both potential and kinetic energy. An example is energy which is the sum of kinetic. Whenever physical scientists discover that a phenomenon appears to violate the law of energy conservation. Heat and work are special cases in that they are not properties of systems, in general we cannot measure how much heat or work are present in an object, but rather only how much energy is transferred among objects in certain ways during the occurrence of a given process. Heat and work are measured as positive or negative depending on which side of the transfer we view them from, the distinctions between different kinds of energy is not always clear-cut. In contrast to the definition, energeia was a qualitative philosophical concept, broad enough to include ideas such as happiness. The modern analog of this property, kinetic energy, differs from vis viva only by a factor of two, in 1807, Thomas Young was possibly the first to use the term energy instead of vis viva, in its modern sense. Gustave-Gaspard Coriolis described kinetic energy in 1829 in its modern sense, the law of conservation of energy was also first postulated in the early 19th century, and applies to any isolated system. It was argued for years whether heat was a physical substance, dubbed the caloric, or merely a physical quantity. In 1845 James Prescott Joule discovered the link between mechanical work and the generation of heat and these developments led to the theory of conservation of energy, formalized largely by William Thomson as the field of thermodynamics
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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 mass from rest 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 by the body in decelerating from its current speed to a state of rest. In classical mechanics, the energy of a non-rotating object of mass m traveling at a speed v is 12 m v 2. In relativistic mechanics, this is an approximation only when v is much less than the speed of light. The standard unit of energy is the joule. The adjective kinetic has its roots in the Greek word κίνησις kinesis, the dichotomy between kinetic energy and potential energy can be traced back to Aristotles concepts of actuality and potentiality. The principle in classical mechanics that E ∝ mv2 was first developed by Gottfried Leibniz and Johann Bernoulli, Willem s Gravesande of the Netherlands provided experimental evidence of this relationship. By dropping weights from different heights into a block of clay, Émilie du Châtelet recognized the implications of the experiment and published an explanation. The terms kinetic energy and work in their present scientific meanings date back to the mid-19th century, early understandings of these ideas can be attributed to Gaspard-Gustave Coriolis, who in 1829 published the paper titled Du Calcul de lEffet des Machines outlining the mathematics of kinetic energy. William Thomson, later Lord Kelvin, is given the credit for coining the term kinetic energy c, energy occurs in many forms, including chemical energy, thermal energy, electromagnetic radiation, gravitational energy, electric energy, elastic energy, nuclear energy, and rest energy. These can be categorized in two classes, potential energy and kinetic energy. Kinetic energy is the movement energy of an object, Kinetic energy can be transferred between objects and transformed into other kinds of energy. Kinetic energy may be best understood by examples that demonstrate how it is transformed to, for example, a cyclist uses chemical energy provided by food to accelerate a bicycle to a chosen speed. On a level surface, this speed can be maintained without further work, except to overcome air resistance, the chemical energy has been converted into kinetic energy, the energy of motion, but the process is not completely efficient and produces heat within the cyclist. The kinetic energy in the moving cyclist and the bicycle can be converted to other forms, for example, the cyclist could encounter a hill just high enough to coast up, so that the bicycle comes to a complete halt at the top. The kinetic energy has now largely converted to gravitational potential energy that can be released by freewheeling down the other side of the hill. Since the bicycle lost some of its energy to friction, it never regains all of its speed without additional pedaling, the energy is not destroyed, it has only been converted to another form by friction
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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, and other factors. The unit for energy in the International System of Units is the joule, the term potential energy was introduced by the 19th century Scottish engineer and physicist William Rankine, although it has links to Greek philosopher Aristotles concept of potentiality. Potential energy is associated with forces that act on a body in a way that the work done by these forces on the body depends only on the initial and final positions of the body in space. These forces, that are called potential forces, can be represented at every point in space by vectors expressed as gradients of a scalar function called potential. Potential energy is the energy of an object. It is the energy by virtue of a position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force that works against the force field of the potential. This work is stored in the field, which is said to be stored as potential energy. If the external force is removed the field acts on the body to perform the work as it moves the body back to the initial position. Suppose a ball which mass is m, and 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 energy, each associated with a particular type of force. Chemical potential energy, such as the energy stored in fossil fuels, is the work of the Coulomb force during rearrangement of mutual positions of electrons and nuclei in atoms and molecules. Thermal energy usually has two components, the energy of random motions of particles and the potential energy of their mutual positions. Forces derivable from a potential are also called conservative forces, the work done by a conservative force is W = − Δ U where Δ U is the change in the potential energy associated with the force. The negative sign provides the convention that work done against a force field increases potential energy, common notations for potential energy are U, V, also Ep. Potential energy is closely linked with forces, in this case, the force can be defined as the negative of the vector gradient of the potential field. If the work for a force is independent of the path, then the work done by the force is evaluated at the start
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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 quantity, impulse is also a vector in the same direction. Impulse applied to an object produces an equivalent vector change in its linear momentum, the SI unit of impulse is the newton second, and 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 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 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 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 and this sort of change is a step change, and is not physically possible. However, this is a model for computing the effects of ideal collisions. The application of Newtons second law for variable mass allows impulse, in the case of rockets, the impulse imparted can be normalized by unit of propellant expended, to create a performance parameter, specific impulse. This fact can be used to derive the Tsiolkovsky rocket equation, which relates the vehicles propulsive change in velocity to the specific impulse. Wave–particle duality defines the impulse of a wave collision, the preservation of momentum in the collision is then called phase matching. Applications include, Compton effect nonlinear optics Acousto-optic modulator Electron phonon scattering Serway, Raymond A. Jewett, John W. Physics for Scientists, Physics for Scientists and Engineers, Mechanics, Oscillations and Waves, Thermodynamics
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Inertia
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Inertia is the resistance of any physical object to any change in its state of motion, this includes changes to its speed, direction, or state of rest. It is the tendency of objects to keep moving in a line at constant velocity. The principle of inertia is one of the principles of classical physics that are used to describe the motion of objects. Inertia comes from the Latin word, iners, meaning idle, Inertia is one of the primary manifestations of mass, which is a quantitative property of physical systems. In common usage, the inertia may refer to an objects amount of resistance to change in velocity, or sometimes to its momentum. Thus, an object will continue moving at its current velocity until some force causes its speed or direction to change. On the surface of the Earth, inertia is often masked by the effects of friction and air resistance, both of which tend to decrease the speed of moving objects, and gravity. Aristotle explained the continued motion of projectiles, which are separated from their projector, by the action of the surrounding medium, Aristotle concluded that such violent motion in a void was impossible. Despite its general acceptance, Aristotles concept of motion was disputed on several occasions by notable philosophers over nearly two millennia, for example, Lucretius stated that the default state of matter was motion, not stasis. Philoponus proposed that motion was not maintained by the action of a surrounding medium, although this was not the modern concept of inertia, for there was still the need for a power to keep a body in motion, it proved a fundamental step in that direction. This view was opposed by Averroes and by many scholastic philosophers who supported Aristotle. However, this view did not go unchallenged in the Islamic world, in the 14th century, Jean Buridan rejected the notion that a motion-generating property, which he named impetus, dissipated spontaneously. Buridans position was that an object would be arrested by the resistance of the air. Buridan also maintained that impetus increased with speed, thus, his 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, buridans thought was followed up by his pupil Albert of Saxony and 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 inherent linear motion of objects, forced into circular motion. The law of inertia states that it is the tendency of an object to resist a change in motion. According to Newton, an object will stay at rest or stay in motion unless acted on by a net force, whether it results from gravity, friction, contact
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Moment of inertia
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It depends on the bodys mass distribution and the axis chosen, with larger moments requiring more torque to change the bodys rotation. It is a property, the moment of inertia of a composite system is the sum of the moments of inertia of its component subsystems. One of its definitions is the moment of mass with respect to distance from an axis r, I = ∫ Q r 2 d m. For bodies constrained to rotate in a plane, it is sufficient to consider their moment of inertia about a perpendicular to the plane. When a body is rotating, or free to rotate, around an axis, the amount of torque needed to cause any given angular acceleration is proportional to the moment of inertia of the body. Moment of inertia may be expressed in units of kilogram metre squared in SI units, moment of inertia plays the role in rotational kinetics that mass plays in linear kinetics - both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, for a point-like mass, the moment of inertia about some axis is given by mr2, where r is the distance to the axis, and m is the mass. For an extended body, the moment of inertia is just the sum of all the pieces of mass multiplied by the square of their distances from the axis in question. For an extended body of a shape and uniform density. In 1673 Christiaan Huygens introduced this parameter in his study of the oscillation of a body hanging from a pivot, the term moment of inertia was introduced by Leonhard Euler in his book Theoria motus corporum solidorum seu rigidorum in 1765, and it is incorporated into Eulers second law. Comparison of this frequency to that of a simple pendulum consisting of a single point of mass provides a mathematical formulation for moment of inertia of an extended body. Moment of inertia appears in momentum, kinetic energy, and in Newtons laws of motion for a rigid body as a physical parameter that combines its shape. There is a difference in the way moment of inertia appears in planar. The moment of inertia of a flywheel is used in a machine to resist variations in applied torque to smooth its rotational output. Moment of inertia I is defined as the ratio of the angular momentum L of a system to its angular velocity ω around a principal axis, if the angular 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 arms or divers curl their bodies into a tuck position during a dive. For a simple pendulum, this yields a formula for the moment of inertia I in terms of the mass m of the pendulum and its distance r from the pivot point as. Thus, moment of inertia depends on both the mass m of a body and its geometry, or shape, as defined by the distance r to the axis of rotation
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Power (physics)
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In physics, power is the rate of doing work. It is the amount of energy consumed per unit time, having no direction, it is a scalar quantity. In the SI system, the unit of power is the joule per second, known as the watt in honour of James Watt, another common and traditional measure is horsepower. Being the rate of work, the equation for power can be written, because this integral depends on the trajectory of the point of application of the force and torque, this calculation of work is said to be path dependent. As a physical concept, power requires both a change in the universe and a specified time in which the change occurs. This is distinct from the concept of work, which is measured in terms of a net change in the state of the physical universe. The output power of a motor is the product of the torque that the motor generates. The power involved in moving a vehicle is the product of the force of the wheels. The dimension of power is divided by time. The SI unit of power is the watt, which is equal to one joule per second, other units of power include ergs per second, horsepower, metric horsepower, and foot-pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the required to lift 550 pounds by one foot in one second. Other units include dBm, a logarithmic measure with 1 milliwatt as reference, food calories per hour, Btu per hour. This shows how power is an amount of energy consumed per unit time. If ΔW is the amount of work performed during a period of time of duration Δt and it is the average amount of work done or energy converted per unit of time. The average power is simply called power when the context makes it clear. The instantaneous power is then the value of the average power as the time interval Δt approaches zero. P = lim Δ t →0 P a v g = lim Δ t →0 Δ W Δ t = d W d t. In the case of constant power P, the amount of work performed during a period of duration T is given by, W = P t
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Work (physics)
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In physics, a force is said to do work if, when acting, there is a displacement of the point of application in the direction of the force. For example, when a ball is held above the ground and then dropped, the SI unit of work is the joule. The SI unit of work is the joule, which is defined as the work expended by a force of one newton through a distance of one metre. The dimensionally equivalent newton-metre is sometimes used as the unit for work, but this can be confused with the unit newton-metre. Usage of N⋅m is discouraged by the SI authority, since it can lead to confusion as to whether the quantity expressed in newton metres is a torque measurement, or a measurement of energy. Non-SI units of work include the erg, the foot-pound, the foot-poundal, the hour, the litre-atmosphere. Due to work having the physical dimension as heat, occasionally measurement units typically reserved for heat or energy content, such as therm, BTU. The work done by a constant force of magnitude F on a point that moves a distance s in a line in the direction of the force is the product W = F s. For example, if a force of 10 newtons acts along a point that travels 2 meters and this is approximately the work done lifting a 1 kg weight from ground level to over a persons head against the force of gravity. Notice that the work is doubled either by lifting twice the weight the distance or by lifting the same weight twice the distance. Work is closely related to energy, the work-energy principle states that an increase in the kinetic energy of a rigid body is caused by an equal amount of positive work done on the body by the resultant force acting on that body. Conversely, a decrease in energy is caused by an equal amount of negative work done by the resultant force. From Newtons second law, it can be shown that work on a free, rigid body, is equal to the change in energy of the velocity and rotation of that body. The work of forces generated by a function is known as potential energy. These formulas demonstrate that work is the associated with the action of a force, so work subsequently possesses the physical dimensions. 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 and this only applies for a single particle system. For example, in an Atwood machine, the rope does work on each body, there are, however, cases where this is not true