Answer
$\omega = (10~\pi)~rad/s$ which is $31.4~rad/s$
Work Step by Step
The line rotates through an angle of $2\pi$ radians 300 times in a time of 60 seconds. We can find the angular speed:
$\omega = \frac{\theta}{t}$
$\omega = \frac{(2\pi~rad)(300)}{60~s}$
$\omega = 10~\pi~rad/s$
$\omega = 31.4~rad/s$