## Precalculus (6th Edition) Blitzer

The angular speed of $20\text{ revolutions per second}$ in radians per second is $\frac{40\pi \ \text{radians}}{\text{second}}$.
The angular speed conversion relation between revolutions per second to radians per second is: $\frac{1\text{ revolution}}{\text{second}}=\frac{2\pi \text{ radians}}{\text{second}}$ Multiply both sides by $20$. \begin{align} & 20\left( \frac{1\text{ revolutions}}{\text{second}} \right)=20\left( \frac{2\pi \text{ radians}}{\text{second}} \right) \\ & 20\text{ revolutions/second}=\frac{40\pi \text{ radians}}{\text{second}} \end{align} Therefore, the angular speed of $20\text{ revolutions per second}$ in radians per second is $\frac{40\pi \ \text{radians}}{\text{second}}$.