For rotational motion about a point or axis, angular velocity is the rate of change of the angular position with time, or in other words the derivative of the angular position with time:

= angular velocity, where *θ*= the angular position*t*= timeThe direction of the angular velocity vector is perpendicular to the plane of rotation as given by the right-hand rule. The angular velocity is expressed in units of [angular distance/time], often radians per second.

For an object moving in a curved path it can be useful to describe the motion using both angular and linear velocities. Using a fundamental relation for circular geometry:

where *θ*= angle*s*= arc subtended by*θ**r*= radius of the circleThe magnitudes of the linear and angular velocities are related by:

where *v*= linear velocity*r*= distance from the axis of rotation*ω*= angular velocityNote that we are not using vector notation in this expression, rather it is the magnitude of the velocities that follow the relation.