Precalculus (6th Edition) Blitzer

The angular speed of $6\text{ revolutions per second}$ is $\frac{12\pi \ \text{radians}}{\text{second}}$.
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 $6$. \begin{align} & 6\left( \frac{1\text{ revolutions}}{\text{second}} \right)=6\left( \frac{2\pi \text{ radians}}{\text{second}} \right) \\ & 6\text{ revolutions/second}=\frac{12\pi \text{ radians}}{\text{second}} \end{align} Therefore, the angular speed of $6\text{ revolutions per second}$ is $\frac{12\pi \ \text{radians}}{\text{second}}$.