# Newton's laws of motion

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Related to Newton's laws of motion: Newton's first law of motion

## motion

motion, the change of position of one body with respect to another. The rate of change is the speed of the body. If the direction of motion is also given, then the velocity of the body is determined; velocity is a vector quantity, having both magnitude and direction, while speed is a scalar quantity, having only magnitude.

### Types of Motion

Uniform motion is motion at a constant speed in a straight line. Uniform motion can be described by a few simple equations. The distance s covered by a body moving with velocity v during a time t is given by s=vt. If the velocity is changing, either in direction or magnitude, it is called accelerated motion (see acceleration). Uniformly accelerated motion is motion during which the acceleration remains constant. The average velocity during this time is one half the sum of the initial and final velocities. If a is the acceleration, vo the original velocity, and vf the final velocity, then the final velocity is given by vf=vo + at. The distance covered during this time is s=vot + 1-2 at2. In the simplest circular motion the speed is constant but the direction of motion is changing continuously. The acceleration causing this change, known as centripetal acceleration because it is always directed toward the center of the circular path, is given by a=v2/r, where v is the speed and r is the radius of the circle.

### The Laws of Motion and Relativity

The relationship between force and motion was expressed by Sir Isaac Newton in his three laws of motion: (1) a body at rest tends to remain at rest or a body in motion tends to remain in motion at a constant speed in a straight line unless acted on by an outside force, i.e., if the net unbalanced force is zero, then the acceleration is zero; (2) the acceleration a of a mass m by an unbalanced force F is directly proportional to the force and inversely proportional to the mass, or a = F/m; (3) for every action there is an equal and opposite reaction. The third law implies that the total momentum of a system of bodies not acted on by an external force remains constant (see conservation laws, in physics). Newton's laws of motion, 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.

Motion at speeds approaching the speed of light must be described by the theory of relativity. The equations derived from the theory of relativity reduce to Newton's when the speed of the object being described is very small compared to that of light. When the motions of extremely small objects (atoms and elementary particles) are described, the wavelike properties of matter must be taken into account (see quantum theory). The theory of relativity also resolves the question of absolute motion. When one speaks of an object as being in motion, such motion is usually in reference to another object which is considered at rest. Although a person sitting in a car is at rest with respect to the car, both in motion with respect to the earth, and the earth is in motion with respect to the sun and the center of the galaxy. All these motions are relative.

It was once thought that there existed a light-carrying medium, known as the luminiferous ether, which was in a state of absolute rest. Any object in motion with respect to this hypothetical frame of reference would be in absolute motion. The theory of relativity showed, however, that no such medium was necessary and that all motion could be treated as relative.

### Bibliography

See J. C. Maxwell, Matter and Motion (1877, repr. 1952).

## Newton's laws of motion

Three fundamental principles which form the basis of classical, or newtonian, mechanics. They are stated as follows:

First law: A particle not subjected to external forces remains at rest or moves with constant speed in a straight line.

Second law: The acceleration of a particle is directly proportional to the resultant external force acting on the particle and is inversely proportional to the mass of the particle.

Third law: If two particles interact, the force exerted by the first particle on the second particle (called the action force) is equal in magnitude and opposite in direction to the force exerted by the second particle on the first particle (called the reaction force).

The newtonian laws have proved valid for all mechanical problems not involving speeds comparable with the speed of light and not involving atomic or subatomic particles. See Dynamics, Force, Kinetics (classical mechanics)

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

## Newton's laws of motion

The three fundamental laws concerning the motion of bodies that were formulated by Isaac Newton and published together with the law of gravitation in Principia, 1687. The laws are
1. Every body continues in a state of rest or of uniform motion in a straight line until that state is changed by the action of a force on the body.
2. The rate of change of linear momentum is proportional to the applied force, F , and occurs in the same direction as that of the force, i.e.
F = d(mv )/dt = m (dv /dt) = ma
where m is the mass, v the velocity, and a the resulting acceleration of the body.
3. Every action is opposed by a reaction of equal magnitude that acts in the opposite direction to the action.

The first law was conceived by Galileo, who first realized the falsity of the Greek notion that a force is required to maintain a body in motion. Newton's laws of motion and of gravitation are fundamental to celestial mechanics.

Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Newton’s Laws of Motion

three laws that form the foundation of classical mechanics. They were formulated by I. Newton in 1687. The first law is: “Every body continues its state of rest or uniform motion in a straight line, except insofar as it is compelled to change that state by an external impressed force.” The second law is: “The rate of change of linear momentum is proportional to the impressed force and takes place in the direction of the straight line along which the force acts.” The third law is: “To every action there is an equal and opposite reaction, or, in other words, the mutual actions between any two bodies are always equal and act in opposite directions.”

Newton’s laws of motion followed from a generalization of numerous observations, experiments, and theoretical investigations conducted by Galileo, C. Huygens, Newton himself, and others.

According to modern concepts and terminology, in the first and second laws the term “body” should be understood to mean a mass point, and “motion” to mean motion with respect to an inertial frame of reference. The mathematical expression of the second law in classical mechanics has the form d(mv)/dt = F, or mw = F, where m is the mass, ν the velocity, and w the acceleration of the point, and F is the impressed force.

Newton’s laws of motion cease to be valid for objects of very small dimensions (elementary particles) and for velocities close to the velocity of light.

### REFERENCES

Galilei, G. “Besedy i matematicheskie dokazatel’stva, kasaiushchiesia dvukh novykh otraslei nauki, otnosiashchikhsia k mekhanike i mestnomu dvizheniiu.” Soch., vol. 1. Moscow-Leningrad, 1934. (Translated from Latin.)
Newton, I. “Matematicheskie nachala natural’noi filosofii.” In A. N. Krylov, Sobr. trudov, vol. 7. Moscow-Leningrad, 1936. (Translated from Latin.)

S. M. TARG

## Newton's laws of motion

[′nüt·ənz ′lȯz əv ′mō·shən]
(mechanics)
Three fundamental principles (called Newton's first, second, and third laws) which form the basis of classical, or Newtonian, mechanics, and have proved valid for all mechanical problems not involving speeds comparable with the speed of light and not involving atomic or subatomic particles.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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