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Encyclopedia > Law of inertia
Newton's First and Second laws, in Latin, from the original 1687 edition of the Principia Mathematica.

Newton's Laws of Motion are three physical laws which provide relationships between the forces acting on a body and the motion of the body, first formulated by Sir Isaac Newton. Newton's laws were first published in his work Philosophiae Naturalis Principia Mathematica (1687). The laws form the basis for classical mechanics. Newton used them to explain many results concerning the motion of physical objects. In the third volume of the text, he showed that the laws of motion, combined with his law of universal gravitation, explained Kepler's laws of planetary motion. Image File history File links Newtons_laws_in_latin. ... Image File history File links Newtons_laws_in_latin. ... Newtons own copy of his Principia, with hand written corrections for the second edition. ... A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. ... In mathematics and statistics, a direct relationship is a positive relationship between two variables in which they both increase or decrease in conjunction. ... In physics, force is an influence that may cause a body to accelerate. ... A physical body is an object which can be described by the theories of classical mechanics, or quantum mechanics, and experimented upon by physical instruments. ... Motion involves change in position, such as this perspective of rapidly leaving Yongsan Station In physics, motion means a continuous change in the position of a body relative to a reference point, as measured by a particular observer in a particular frame of reference. ... Sir Isaac Newton, FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, alchemist, and natural philosopher, regarded by many as the greatest figure in the history of science. ... Newtons own copy of his Principia, with handwritten corrections for the second edition. ... Events March 19 - The men under explorer Robert Cavelier de La Salle murder him while searching for the mouth of the Mississippi River. ... Mechanics (Greek ) is the branch of physics concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effect of the bodies on their environment. ... Isaac Newtons theory of universal gravitation states the following: Every single point mass attracts every other point mass by a force heading along the line combining the two. ... This article does not cite its references or sources. ...

## The Three Laws of Motion GA_googleFillSlot("encyclopedia_square");

Newton's Laws of Motion describe only motion of a body as a whole and are valid only for motions relative to a reference frame. The following are brief modern formulations of Newton's three laws of motion:

First Law
A body at rest remains at rest, and a body in motion continues to move in a straight line with a constant speed unless and until an external unbalanced force acts upon it.
Second Law
The rate of change of momentum of a body is directly proportional to the impressed force and takes place in the direction in which the force acts.
Third Law
To every action (force applied) there is an equal and opposite reaction (equal force in the opposite direction).
Another way of stating Newton's third law is that if object A exerts a force on object B, then object B exerts a force of the same magnitude on A, in the opposite direction.

It is important to note that these three laws together with his law of gravitation provide a satisfactory basis for the explanation of motion of everyday macroscopic objects under everyday conditions. However, when applied to extremely high speeds or extremely small objects, Newton's laws break down; this was remedied by Albert Einstein's Special Theory of Relativity for high speeds and by quantum mechanics for small objects. Macroscopic is commonly used to describe physical objects that are measurable and observable by the naked eye. ... Einstein redirects here. ... The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest... Fig. ...

## Newton's first law: law of inertia

Lex I: Corpus omne perseverare in statu suo quiescendi vel movendi uniformiter in directum, nisi quatenus a viribus impressis cogitur statum illum mutare.

An object at rest will remain at rest unless acted upon by an external and unbalanced force. An object in motion will remain in motion unless acted upon by an external and unbalanced force.

This law is also called the law of inertia. The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. ...

The net force on an object is the vector sum of all the forces acting on the object. Newton's first law says that if this sum is zero, the state of motion of the object does not change. Essentially, it makes the following two points: A vector in physics and engineering typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but in this...

• An object that is not moving will not move until a net force acts upon it.
• An object that is in motion will not change velocity (accelerate) until a net force acts upon it.

The first point seems relatively obvious to most people, but the second may take some thinking through, because we have no experience in every-day life of things that keep moving forever (except celestial bodies). If one slides a hockey puck along a table, it doesn't move forever, it slows and eventually comes to a stop. But according to Newton's laws, this is because a force is acting on the hockey puck and, sure enough, there is frictional force between the table and the puck, and that frictional force is in the direction opposite the movement. It is this force which causes the object to slow to a stop. In the absence of such a force, as approximated by an air hockey table or ice rink, the puck's motion would not slow. Newton's first law is just a restatement of what Galileo had already described and Newton gave credit to Galileo. It differs from Aristotle's view that all objects have a natural place in the universe. Aristotle believed that heavy objects like rocks wanted to be at rest on the Earth and that light objects like smoke wanted to be at rest in the sky and the stars wanted to remain in the heavens. Galileo can refer to: Galileo Galilei, astronomer, philosopher, and physicist (1564 - 1642) the Galileo spacecraft, a NASA space probe that visited Jupiter and its moons the Galileo positioning system Life of Galileo, a play by Bertolt Brecht Galileo (1975) - screen adaptation of the play Life of Galileo by Bertolt Brecht... Aristotle (Greek: AristotÃ©lÄ“s) (384 BC â€“ March 7, 322 BC) was an ancient Greek philosopher, a student of Plato and teacher of Alexander the Great. ...

However, a key difference between Galileo's idea from Aristotle's is that Galileo realized that force acting on a body determines acceleration, not velocity. This insight leads to Newton's First Law - no force means no acceleration, and hence the body will continue to maintain its velocity.

The Law of Inertia apparently occurred to many different natural philosophers independently. Inertia of motion was described in the third century BCE in the Mo Tzu, a collection of Chinese philosophical texts, and the 17th century philosopher René Descartes also formulated the law, although he did not perform any experiments to confirm it. Mozi (c. ... RenÃ© Descartes (March 31, 1596 â€“ February 11, 1650), also known as Renatus Cartesius (latinized form), was a highly influential French philosopher, mathematician, and scientist. ...

There are no perfect demonstrations of the law, as friction usually causes a force to act on a moving body, and even in outer space gravitational forces act and cannot be shielded against, but the law serves to emphasize the elementary causes of changes in an object's state of motion: forces. Friction is the force that opposes the relative motion or tendency of such motion of two surfaces in contact. ...

## Newton's second law: historical development

Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa imprimitur.

The rate of change of momentum of a body is proportional to the resultant force acting on the body and is in the same direction.

In an exact original 1792 translation (from Latin) Newton's Second Law of Motion reads:

LAW II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. — If a force generates a motion, a double force will generate double the motion, a triple force triple the motion, whether that force be impressed altogether and at once, or gradually and successively. And this motion (being always directed the same way with the generating force), if the body moved before, is added to or subtracted from the former motion, according as they directly conspire with or are directly contrary to each other; or obliquely joined, when they are oblique, so as to produce a new motion compounded from the determination of both.

Here Newton is saying that the rate of change in the momentum of an object is directly proportional to the amount of force exerted upon the object. He also states that the change in direction of momentum is determined by the angle from which the force is applied.

However, it must be remembered that for Newton, mass was constant and independent of velocity. To take "motion" (motu) as meaning momentum gives a false impression of what Newton believed. Since he took mass as constant (part of the constant of proportionality) it can, in modern notation, be taken to the left of the derivative as . If m is dependent on velocity (and thus indirectly upon time) as we would now hold, then m has to be included in the derivative, giving or .

Using momentum in the terminology (which would never have occurred to Newton) is a latter-day revision of the law to bring it into correspondence with special relativity. The special theory of relativity was proposed in 1905 by Albert Einstein in his article On the Electrodynamics of Moving Bodies. Some three centuries earlier, Galileos principle of relativity had stated that all uniform motion was relative, and that there was no absolute and well-defined state of rest...

Interestingly, Newton is restating in his further explanation another prior idea of Galileo, what we call today the Galilean transformation or the addition of velocities.

An interesting fact when studying Newton's Laws of Motion from the Principia is that Newton himself does not explicitly write formulae for his laws which was common in scientific writings of that time period. In fact, it is today commonly added when stating Newton's second law that Newton has said, "and inversely proportional to the mass of the object." This however is not found in Newton's second law as directly translated above. In fact, the idea of mass is not introduced until the third law.

In mathematical terms, the differential equation can be written as:

where is force, is mass, is velocity, is time and is the constant of proportionality. The product of the mass and velocity is the momentum of the object. In physics, force is an influence that may cause a body to accelerate. ... Unsolved problems in physics: What causes anything to have mass? Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... The velocity of an object is simply its speed in a particular direction. ... A pocket watch, a device used to measure time Two distinct views exist on the meaning of time. ... This article is about proportionality, the mathematical relation. ... Unsolved problems in physics: What causes anything to have mass? Mass is a property of a physical object that quantifies the amount of matter and energy it is equivalent to. ... The velocity of an object is simply its speed in a particular direction. ... In classical mechanics, momentum (pl. ...

If mass of an object in question is known to be constant and using the definition of acceleration, this differential equation can be rewritten as: Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point In physics or physical science, acceleration (symbol: a) is defined as the rate of change (or derivative with respect to...

where is the acceleration. Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point In physics or physical science, acceleration (symbol: a) is defined as the rate of change (or derivative with respect to...

Using only SI Units for the definition of Newton, the constant of proportionality is unity (1). Hence: The International System of Units (symbol: SI) (for the French phrase Système International dUnités) is the most widely used system of units. ... The newton (symbol: N) is the SI unit of force. ... This article is about proportionality, the mathematical relation. ...

However, it has been a common convention to describe Newton's second law in the mathematical formula where is Force, is acceleration and is mass. This is actually a combination of laws two and three of Newton expressed in a very useful form. This formula in this form did not even begin to be used until the 18th century, after Newton's death, but it is implicit in his laws.

Newton's Third Law of Motion states:

LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts. -- Whatever draws or presses another is as much drawn or pressed by that other. If you press a stone with your finger, the finger is also pressed by the stone. If a horse draws a stone tied to a rope, the horse (if I may so say) will be equally drawn back towards the stone: for the distended rope, by the same endeavour to relax or unbend itself, will draw the horse as much towards the stone, as it does the stone towards the horse, and will obstruct the progress of the one as much as it advances that of the other. If a body impinge upon another, and by its force change the motion of the other, that body also (because of the equality of the mutual pressure) will undergo an equal change, in its own motion, toward the contrary part. The changes made by these actions are equal, not in the velocities but in the motions of the bodies; that is to say, if the bodies are not hindered by any other impediments. For, because the motions are equally changed, the changes of the velocities made toward contrary parts are reciprocally proportional to the bodies. This law takes place also in attractions, as will be proved in the next scholium.

The explanation of mass is expressed here for the first time in the words "reciprocally proportional to the bodies" which have now been traditionally added to Law 2 as "inversely proportional to the mass of the object." This is because Newton in his definition 1 had already stated that when he said "body" he meant "mass". Thus we arrive at . When the formula is taken into account, Law II can be also interpreted as a quantitative restatement of Law I, where mass also acts as a measurement of inertia.

## Newton's third law: law of reciprocal actions

Newton's third law. The skaters' forces on each other are equal in magnitude, and in opposite directions

Lex III: Actioni contrariam semper et æqualem esse reactionem: sive corporum duorum actiones in se mutuo semper esse æquales et in partes contrarias dirigi. Image File history File links Skaters_showing_newtons_third_law. ... Image File history File links Skaters_showing_newtons_third_law. ...

All forces occur in pairs, and these two forces are equal in magnitude and opposite in direction.

This law of motion is most commonly paraphrased as: "For every action force there is an equal, but opposite, reaction force."

The third law follows mathematically from the law of conservation of momentum. In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...

As shown in the diagram opposite, the skaters' forces on each other are equal in magnitude, and opposite in direction. Although the forces are equal, the accelerations are not: the less massive skater will have a greater acceleration due to Newton's second law. It is important to note that the action/reaction pair act on different objects and do not cancel each other out.

If a basketball hits the ground, the basketball's force on the Earth is the same as Earth's force on the basketball. However, due to the ball's much smaller mass, Newton's second law predicts that its acceleration will be much greater than that of the Earth. Not only do planets accelerate toward stars, but stars also accelerate toward planets. If a star gravitationally attracts a planet, then the planet will gravitationally attract the star. Usually the planet is less massive than the star and thus displays greater changes in it's state of motion. Similarly, if a falling ball is pulled towards the Earth, then the reaction force is that the Earth is pulled toward the ball. We can not detect any change in the Earth's motion because it is much more massive than the ball. This article is about the astronomical object. ...

The two forces in Newton's third law are of the same type, e.g., if the road exerts a forward frictional force on an accelerating car's tires, then it is also a frictional force that Newton's third law predicts for the tires pushing backward on the road.

## Importance and range of validity

Newton's laws were verified by experiment and observation for over 200 years, and they are excellent approximations at the scales and speeds of everyday life. Newton's laws of motion, together with his law of universal gravitation and the mathematical techniques of calculus, provided for the first time a unified quantitative explanation for a wide range of physical phenomena. This article covers the physics of gravitation. ... Calculus is the name given to a group of systematic methods of calculation, computation, and analysis in mathematics which use a common and specialized algebraic notation. ...

According to Einstein's theory of relativity, there is no preferred frame of reference. The laws of physics are equally valid in all frames of reference. Motion can only be measured relative to a frame of reference. According to the equivalence principle, an observer on the surface of the Earth could not find any difference (in the first order) between the gravitational attraction of earth and the inertial force that he feels when he is in a rocket in outer space that accelerates upwards (from the standpoint of the observer) at 9.8 m/s2. In other words, he may regard any inertial force as a gravitational force. Consequently, Newton's laws of motion are only valid in an inertial frame of reference. Notice that the surface of the Earth does not define an inertial frame of reference because it is rotating and orbiting and because of Earth's gravity. However, since the speed of rotation and revolution change relatively slowly, the inertial force is tiny. Therefore, Newton's laws of motion remain a good approximation on earth. In a non-inertial frame of reference, inertial forces must be considered for Newton's laws to remain valid. Einstein redirects here. ... Two-dimensional analogy of space-time distortion described in General Relativity. ... In relativity, the equivalence principle is applied to several related concepts dealing with gravitation and the uniformity of physical measurements in different frames of reference. ... An inertial reference frame is a reference frame which does not accelerate. ...

In quantum mechanics concepts such as force, momentum, and position are defined by linear operators that operate on the quantum state; at speeds that are much lower than the speed of light, Newton's laws are just as exact for these operators as they are for classical objects. At speeds comparable to the speed of light, the second law holds in the original form F = dp / dt, which says that the force is the derivative of the momentum of the object with respect to time, but some of the newer versions of the second law (such as the constant mass approximation above) do not hold at relativistic velocities. Fig. ... In mathematical formulations of quantum mechanics, an operator is a linear transformation from a Hilbert space to itself. ... A quantum state is any possible state in which a quantum mechanical system can be. ...

To sum it up in an easy way to remember, Newton’s third law of motion can be defined as follows: (For every action there is a reaction equal in magnitude and opposite in direction)

## Relationship to the conservation laws

The laws of conservation of momentum, energy, and angular momentum are of more general validity than Newton's laws, since they apply to both light and matter, and to both classical and non-classical physics. In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... In classical mechanics, momentum (pl. ... Gyroscope. ...

Because force is the time derivative of momentum, the concept of force is redundant and subordinate to the conservation of momentum, and is not used in fundamental theories (e.g. quantum mechanics, quantum electrodynamics, general relativity, etc.). The standard model explains in detail how the three fundamental forces known as gauge forces originate out of exchange by virtual particles. Other forces such as gravity and fermionic degeneracy pressure arise from conditions in the equations of motion in the underlying theories. Fig. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... The Standard Model of Fundamental Particles and Interactions For the Standard Model in Cryptography, see Standard Model (cryptography). ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In the description of the interaction between elementary particles in quantum field theory, a virtual particle is a temporary elementary particle, used to describe an intermediate stage in the interaction. ... Gravity redirects here. ... The Pauli exclusion principle is a quantum mechanical principle formulated by Wolfgang Pauli in 1925, which states that no two identical fermions may occupy the same quantum state simultaneously. ...

Conservation of energy was discovered nearly two centuries after Newton's lifetime, the long delay occurring because of the difficulty in understanding the role of microscopic and invisible forms of energy such as heat and infra-red light.

This is a list of scientific laws named after people (eponymous laws). ... Note: This article contains special characters. ... Galilean invariance is a principle which states that the fundamental laws of physics are the same in all inertial (uniform-velocity) frames of reference. ... General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... In physics, Modified Newtonian Dynamics (MOND) is a theory that explains the galaxy rotation problem without assuming the existence of dark matter. ... Lagrangian mechanics is a re-formulation of classical mechanics introduced by Joseph Louis Lagrange in 1788. ... The principle of least action was first formulated by Pierre-Louis Moreau de Maupertuis, who said that Nature is thrifty in all its actions. See action (physics). ...

## References

• Marion, Jerry and Thornton, Stephen. Classical Dynamics of Particles and Systems. Harcourt College Publishers, 1995. ISBN 0-03-097302-3
• Fowles, G. R. and Cassiday, G. L. Analytical Mechanics (6ed). Saunders College Publishing, 1999. ISBN 0-03-022317-2

Results from FactBites:

 Inertia - Wikipedia, the free encyclopedia (2964 words) The principle of inertia is one of the fundamental laws of classical physics which are used to describe the motion of matter and how it is affected by applied forces. Physics and mathematics appear to be less inclined to use the original concept of inertia as "a tendency to maintain momentum" and instead favor the mathematically useful definition of inertia as the measure of a body's resistance to changes in momentum or simply a body's inertial mass. Thus, "mass is the quantitative or numerical measure of body’s inertia, that is of its resistance to being accelerated".
 CATHOLIC ENCYCLOPEDIA: Law (4389 words) Human laws, however, must be subordinate to the Divine law, or at least, must not contradict it, for human authority is only a participation in the supreme Divine power of government, and it is impossible that God could give human beings the right to issue laws that are unreasonable and in contravention of His will. Law is a bond imposed upon the subjects by which their will is bound or in some way brought under compulsion in regard to the performance or the omission of definite actions. A classification of law, as limited to law administered in the courts, and familiar to Roman jurisprudence, is that of law in the strict sense and equity (jus strictum et jus aequum et bonum).
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