Answer
It makes $~~8.3~~$ revolutions in this time.
Work Step by Step
We can find the angular acceleration:
$\omega_f = \omega_0+\alpha~t$
$\alpha = \frac{\omega_f - \omega_0}{t}$
$\alpha = \frac{0 - 33~\frac{1}{3}~rev/min}{0.50~min}$
$\alpha = -66~\frac{2}{3}~rev/min^2$
We can find $\theta$:
$\theta = \omega_0~t+\frac{1}{2}\alpha~t^2$
$\theta = (33\frac{1}{3}~rev/min)(0.50~min)+\frac{1}{2}(-66~\frac{2}{3}~rev/min^2)~(0.50~min)^2$
$\theta = 8.3~rev$
It makes $~~8.3~~$ revolutions in this time.
