Difference Between Velocity and Acceleration
Velocity is the distance an object travels in a specified direction during a unit of time. Velocity thus differs from speed, for which the direction is unspecified. Because velocity is a vector quantity (, it has two components: a magnitude, or speed of motion, and a direction of motion. The velocity of an object may vary from one moment to the next if either the speed or the direction of motion changes, or if both change at the same time. Either variation is an acceleration. For example, an object revolving in a circle undergoes acceleration. It may have constant angular (rotative) speed, but its direction of motion constantly changes.
Acceleration, 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 (m/sec2). 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 ever-increasing 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.