angular velocity, time rate at which an objectrotates, or revolves, about anaxis, or at which theangular displacement between two bodies changes. In thefigure, this displacement is represented by the angleθ between a line on one body and a line on the other.

In engineering, angles or angular displacements are commonly expressed in degrees or revolutions (of 360°), and angular velocities in revolutions per minute (rpm). In mathematics andphysics, angles are usually expressed in radians and angular velocities in radians per second. These measures are related through the following conversion factors: 1 degree equalsπ/180 (about 0.0175) radian; 1 rpm equalsπ/30 (about 0.105) radian per second.

In many situations, an angular velocity—usually symbolized by the Greek letteromega (ω)—is equally well regarded as afrequency, and the choice of terms depends upon the particular aspect of a system being considered. Thus, in electrical engineering, the rotational speed of a generator might be expressed in revolutions per minute, whereas the alternatingelectric current produced by the generator would be described in terms of its frequency.

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Theangular acceleration is the time rate of change of the angular velocity and is usually designated byα and expressed in radians per second per second. For the case in which the angular velocity is uniform (nonvarying),θ =ωt andα = 0. Ifα is uniform but not zero,ω =αt andθ =1/2αt².