Rotational motion can be described by an angular position $\theta$ measured about a chosen axis.

Angles are normally measured in radians because radians connect rotation directly to arc length.

Angular displacement

If the angular position changes from $\theta_i$ to $\theta_f$, the angular displacement is

$$\Delta\theta=\theta_f-\theta_i.$$

The sign depends on the chosen positive direction of rotation, commonly counterclockwise.

Average angular velocity

Over a time interval $\Delta t$, the average angular velocity is

$$\bar\omega=\frac{\Delta\theta}{\Delta t}.$$

Its SI unit is radians per second.

Linear and angular motion

For a point at distance $r$ from the rotation axis, angular displacement corresponds to arc length

$$s=r\theta.$$

When the point rotates rigidly with angular speed $\omega$, its tangential speed is

$$v=r|\omega|.$$

All points of a rigid body share the same angular velocity about the axis, but points farther from the axis move through larger linear distances in the same time.

Angular position and angular velocity are the rotational counterparts of linear position and velocity.