Answer
The angular speed is $2\pi~rad/day$ which is $0.2618~rad/hr$
Work Step by Step
The earth rotates through an angle of $2\pi$ radians in 24 hours. We can find the angular speed:
$\omega = \frac{2\pi~rad}{24~hrs}$
$\omega = \frac{\pi~rad}{12~hrs}$
$\omega = 0.2618~rad/hr$
The angular speed is $2\pi~rad/day$ which is $0.2618~rad/hr$