Angular Velocity

Suppose (see Fig. 11-4) that our rotating body is at angular position at time and at angular position at time . We define the average angularvelocityof the body in the time interval from to to be

11 -5

in which is the angular displacement that occurs during ( is the lowercase Greek letter omega).

The (instantaneous) angular velocity, with which we shall be most concemed, is the limit of the ratio in Eq. 11 -5 as approaches zero. Thus,

11 -6

If we know , we can find the angular velocity by differentiation.

Fig. 11-4

Equations 11-5 and 11-6 hold not only for the rotating rigid body as a whole but also for every particle of that body because the particles are all locked together. The unit of angular velocity is commonly the radian per second (rad/s) or the revolution per second (rev/s).

If a particle moves in translation along an axis, its linear velocity is either positive or negative, depending on whether the particle is moving in the positive or negative direction of the axis. Similarly, the angular velocity of a rotating rigid body is either positive or negative, depending on whether the body is rotating counterclockwise (positive) or clockwise (negative). The magnitude of an angular velocity is called the angular speed,which is also represented with .