Answer
$1.59 \; revolutions\; per \; second$.
Work Step by Step
The given values are
Angular velocity $=10.0\; rad\; per \; second$.
We know that $2\pi \; rad = 1 \; revolution$.
Therefore $1\; rad = \frac {1}{2\pi} \; revolution$
Or we can write
$1\; rad \; per \; second= \frac {1}{2\pi} \; revolutions\; per \; second$
Multiply both sides by $10.0$
$10.0\; rad \; per \; second= \frac {10.0}{2\pi} \; revolutions\; per \; second$
Simplify.
$10.0\; rad \; per \; second= \frac {5}{\pi} \; revolutions; per \; second$
This gives:
$10.0\; rad \; per \; second= 1.59 \; revolutions\; per \; second$.
