Answer
The angular speed of pulley B' is $~~15~rad/s$
Work Step by Step
We can find the linear speed of a point on belt 1:
$v = \omega_A~R_A$
$v = (10~rad/s)(0.15~m)$
$v = 1.5~m/s$
We can find the angular speed of pulley B:
$\omega_B = \frac{v}{R_B}$
$\omega_B = \frac{1.5~m/s}{0.10~m}$
$\omega_B = 15~rad/s$
The angular speed of pulley B is $~~15~rad/s$
Since pulley B' is rigidly attached to pulley B, they have the same angular speed.
The angular speed of pulley B' is $~~15~rad/s$
