Answer
$17 \ min^{-1}$
Work Step by Step
We know that the gravitational and frictional forces must be at least equal. Thus:
$mg = \mu F_n$
We know that the normal force is the centripetal force, so it follows:
$mg = \frac{\mu mv^2}{r} \\ v =\sqrt{\frac{gr}{\mu}}=\sqrt{\frac{(9.81)(5.1)}{.62}}=8.98 \ m/s$
We convert this to rotations per minute:
$\omega=\frac{v}{r}=\frac{8.98 \ m/s}{5.1}=1.76\ rads/s = 17 \ min^{-1}$
