## Precalculus (6th Edition) Blitzer

The angular velocity of the point is $\frac{\pi }{12}$ radians per hour, which means that the point rotates $\frac{\pi }{12}$ radians in one hour. The rotation of the point in 24 hours is \begin{align} & \left( 24 \right)\frac{\pi }{12}\ \text{rad}=\frac{24\pi }{12}\ \text{rad} \\ & =2\pi \ \text{rad} \end{align} Hence, the point will complete one full revolution in 24 hours because $2\pi$ radians is the measure of one full revolution.