# Newton's laws of motion

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## Newton's laws of motion:

see 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

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## 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)

## 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*)/d

*t*=

*m*(d

*v*/d

*t*) =

*ma*

*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.

## 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.)

See also references under MECHANICS.

S. M. TARG