Answer
The angular speed of the larger pulley is 4.36 rad/s
The angular speed of the smaller pulley is 8.18 rad/s
Work Step by Step
We can find the angular speed of the larger pulley:
$\omega = \frac{\theta}{t}$
$\omega = \frac{(2\pi~rad)(25)}{36~s}$
$\omega = 4.36~rad/s$
We can find the linear speed of the larger pulley:
$v = \omega ~r$
$v = (4.36~rad/s)(15~cm)$
$v = 65.4~cm/s$
Since the same belt goes around both pulleys, we know that both pulleys have the same linear speed. We can find the angular speed of the smaller pulley:
$\omega = \frac{v}{r}$
$\omega = \frac{65.4~cm/s}{8~cm}$
$\omega = 8.18~rad/s$
