## Physics: Principles with Applications (7th Edition)

(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.
$\omega_0 = (850 ~rev/min)(2\pi)(\frac{1 ~min}{60 ~s})$ $\omega_0 = 89 ~rad/s$ $\theta = (1250 ~rev)(2\pi) = 7900 ~rad$ (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.