Answer
$\alpha = 420~rad/s^2$
Work Step by Step
We can find the angular acceleration:
$\tau = I~\alpha$
$\alpha = \frac{\tau}{I}$
$\alpha = \frac{r~F}{I}$
$\alpha = \frac{(r)(0.50t+0.30t^2)}{I}$
$\alpha = \frac{(0.10~m)[(0.50)(3.0~s)+(0.30)(3.0~s)^2]}{1.0\times 10^{-3}~kg~m^2}$
$\alpha = 420~rad/s^2$
