Answer
The angular speed of the pulley is 0.24 rad/s
Work Step by Step
We can find the linear speed of the belt:
$v = \frac{d}{t}$
$v = \frac{56~cm}{18~s}$
$v = 3.1~cm/s$
The linear speed of the belt is 3.1 cm/s
We can find the angular speed of the pulley:
$\omega = \frac{v}{r}$
$\omega = \frac{3.1~cm/s}{12.96~cm}$
$\omega = 0.24~rad/s$
The angular speed of the pulley is 0.24 rad/s