Answer
(a) The ball has turned through 18.5 revolutions.
(b )The ball's angular speed is $18.1~rad/s$
Work Step by Step
(a) We can find the angle $\theta$ through which the ball has rotated:
$\theta = \frac{d}{r} = \frac{18~m}{0.155~m} = 116~rad$
We can convert from units of radians to revolutions:
$116~rad \times \frac{1~rev}{2\pi~rad} = 18.5~rev$
The ball has turned through 18.5 revolutions.
(b) We can find the ball's angular speed:
$\omega = \frac{v}{r} = \frac{2.8~m/s}{0.155~m} = 18.1~rad/s$
The ball's angular speed is $18.1~rad/s$.
