Answer
The angular speed of the Ferris wheel is $0.087 ~rad/s$
Work Step by Step
The Ferris wheel rotates through an angle of $\frac{5\pi}{6}~rad$ in a time of 30 seconds. We can find the angular speed:
$\omega = \frac{\theta}{t}$
$\omega = \frac{\frac{5\pi}{6}~rad}{30~s}$
$\omega = 0.087~rad/s$
The angular speed of the Ferris wheel is $0.087 ~rad/s$