Answer
(a) The angular acceleration $\alpha$ was $-0.50 ~rad/s^2$
(b) It took 178 seconds for the fan to come to a complete stop.
Work Step by Step
$\omega_0 = (850 ~rev/min)(2\pi)(\frac{1 ~min}{60 ~s})$
$\omega_0 = 89 ~rad/s$
$\theta = (1250 ~rev)(2\pi) = 7900 ~rad$
(a) We can use $\omega_0$ and $\theta$ to find the angular acceleration $\alpha$:
$\alpha = \frac{\omega^2-\omega_0^2}{2\theta} =
\frac{0-(89 ~rad/s)^2}{(2)(7900 ~rad)} = -0.50 ~rad/s^2$
The angular acceleration $\alpha$ was $-0.50 ~rad/s^2$.
(b) $t = \frac{\omega - \omega_0}{a} = \frac{0 - 89 ~rad/s}{-0.50 ~rad/s^2} = 178 ~s$
Therefore, it took 178 seconds for the fan to come to a complete stop.