Answer
(a) $t = 24.0~s$
(b) The blade turns 68.8 revolutions.
Work Step by Step
(a) $\omega = \alpha ~t$
$t = \frac{\omega}{\alpha}$
$t = \frac{36.0~rad/s}{1.50~rad/s^2}$
$t = 24.0~s$
(b) $\theta = \frac{1}{2}~\alpha~t^2$
$\theta = \frac{1}{2}(1.50~rad/s^2)(24.0~s)^2$
$\theta = 432~rad$
Let $n$ be the number of revolutions.
$n = \frac{\theta}{2 \pi ~rad/rev} = \frac{432~rad}{2 \pi~rad/rev}$
$n = 68.8~revolutions$
The blade turns 68.8 revolutions.
