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Columbia University Press
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).