ACCELERATION, is the rate at which a velocity changes. There are two principal types of acceleration, linear acceleration and angular acceleration.
A linear velocity, measured for example in miles per hour (mph) or meters per second (m/sec), can change in amount or magnitude, or it can change in direction. Either of these changes in linear velocity produces a linear acceleration, measured for example in meters per second per second (). Thus, an automobile travelling in a given direction experiences a linear acceleration whenever it speeds up or slows down. The same automobile, when driven around a curve, also experiences a linear acceleration by virtue of the change in its direction of motion.
When a phonograph record revolves about a vertical axis, its rotational speed is usually measured in revolutions per minute (rpm) or revolutions per second (rev/sec). A line drawn from the center of the rotating disk to any other point on the disk rotates along with the disk, sweeping out an everincreasing angle as it turns. After one revolution, it has swept out an angle of 360° or 2π radians (rad); after two revolutions, 720° or 4π rad; and so forth. The angular speed of the rotating disk is the angle swept through by the rotating line per unit time, and is usually measured in degrees per second or in radians per second. Angular speed in radians per second is always equal to the constant 2π times the rotational speed in revolutions per second.
Angular velocity is a vector quantity; that is, it, has both magnitude and direction. For any rotating body, the size or magnitude of its angular velocity is simply its angular speed. The direction of its angular velocity is taken by convention as pointing along its axis of rotation. Angular acceleration is the rate of change of angular velocity. Thus, a top experiences angular acceleration when it is “whipped” into motion, when it slows down, and when its axis of rotation exhibits a wobble.
Linear and angular acceleration can be illustrated by considering an object whirling at the end of a string around a fixed center. The string connecting the object to the center sweeps out some angle in a unit time as the object traverses a corresponding distance along the arc of the circle. Thus, the angular speed of the object in radians per second is proportional to the linear speed of the object. If the object moves in the circle at constant speed, its angular acceleration is zero, although it continually undergoes a linear acceleration because it is continually changing its direction of motion toward the center of the circle. Such a linear acceleration is called a centripetal acceleration. If the object moves on the circle with changing speed, it experiences an additional acceleration along the line of its motion, called a tangential acceleration; for a given length of string, the body’s angular acceleration is proportional to its tangential acceleration.
For a discussion of the relationship of acceleration to force and of the acceleration caused by the attraction of one mass for another.