Answer
$\alpha = -7.66~rad/s^2$
Work Step by Step
We can find the angular acceleration:
$\omega = \omega_0+\alpha~t$
$0 = \omega_0+\alpha~t$
$\alpha = \frac{-\omega_0}{t}$
$\alpha = \frac{-(39.0~rev/s)(2\pi~rad)}{32.0~s}$
$\alpha = -7.66~rad/s^2$