Answer
20 minutes
Work Step by Step
We find:
$\alpha = \frac{\tau}{I}=\frac{rF}{\frac{1}{2}mr^2}=\frac{.205\times34,000}{.5(7.7\times10^4)(2.4^2)}=.0314\ rads/s^2$
Converting the rotation speed to radians per second, we find:
$37.699/.0314=1200\ s =\fbox{20 minutes}$
