Answer
larger pulley $ \frac{25\pi}{18}\ rad/sec$,
smaller pulley $\frac{125\pi}{48}\ rad/sec$.
Work Step by Step
1. We can find the angular speed of the larger pulley as $\omega_1=\frac{25\times2\pi}{36}=\frac{25\pi}{18}\ rad/sec$
2. The linear speed of the belt is the same at the two pulleys, we have $r_1\omega_1=r_2\omega_2$ or $15\times\frac{25\pi}{18}=8\omega_2$, thus we have $\omega_2=\frac{125\pi}{48}\ rad/sec$ for the smaller pulley.
