Angular Velocity and Acceleration

Definition: Angular Velocity

Angular velocity $\omega$ of a rigid body is the rate of change of its angular position. Thus, if $\theta$ = $\theta_{1}^{}$ at t = t₁ , and $\theta$ = $\theta_{2}^{}$ at t = t₂ , then the average angular velocity of the body over the time interval $\Delta$t = t₂ - t₁ is:

$$\overline{\omega} {\theta_2- \theta_1\over t_2-t_1} {\Delta \theta \over \Delta t}$$ (4)

As for linear motion, the instantaneous velocity is obtained by making the time interval very small:

$$\omega {\Delta \theta \over \Delta t}$$ (5)

The units of angular velocity are most conveniently given in rads/sec, but can also be expressed in revolutions/sec or degrees/sec using the conversions given above.

Definition: Angular Acceleration

Angular Acceleration is the rate of change of angular velocity with time. The average angular acceleration of a rigid body over a time interval $\Delta$t = t₂ - t₁ is:

$$\overline{\alpha}$$ (6)

The instantaneous angular acceleration is obtained by taking a very small time interval:

$$\alpha \lim_{\Delta t\to 0}^{} {\Delta \omega \over \Delta t}$$ (7)

The units of angular acceleration are normally radians/sec ².