Answer
The angular speed of $6\text{ revolutions per second}$ is $\frac{12\pi \ \text{radians}}{\text{second}}$.
Work Step by Step
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 $\frac{12\pi \ \text{radians}}{\text{second}}$.
