Angular velocity

Also called Angular speed

Angular velocity is the rate at which angular position changes with time, measured in radians per second. Every point on a rigid rotating system shares the same angular velocity, however far from the axis of rotation it sits.

Angular velocity does for a rotation what velocity does for straight-line motion. EK 5.1.A.2 defines the average value as the average rate at which angular position changes with respect to time:

\omega_{\text{avg}} = \frac{\Delta\theta}{\Delta t}

Units are radians per second. The sign follows whichever direction of rotation you declared positive.

One rigid body, one value. EK 5.2.A.3 says all points within a rigid system have the same angular velocity and the same angular acceleration. That is what makes angular quantities worth having: a spinning disk has a single $\omega$ , while every point on it has a different linear speed.

Tangential speed is the linear partner. A point a perpendicular distance $r$ from the axis moves at

v = r\omega

printed on both the AP Physics 1 and the AP Physics C: Mechanics equation sheets. Double the radius at fixed $\omega$ and you double the speed, which is why the rim of a wheel outruns the hub. The relation is only valid with $\omega$ in radians per second.

Angular speed and angular velocity are used interchangeably at AP Physics 1, because the Topic 5.1 boundary statement restricts direction to clockwise or counterclockwise rather than treating $\omega$ as a vector.

For the equations that link $\omega$ to time, angle and angular acceleration, see rotational kinematics.

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