Answer
(a) The ball rolls through an angle of $6.0~rad$
(b) The ball's angular speed is $1.4~rad/s$
Work Step by Step
(a) We can find the angle $\theta$ through which the ball rolls:
$\theta = \frac{d}{r} = \frac{15~cm}{2.5~cm} = 6.0~rad$
The ball rolls through an angle of $6.0~rad$
(b) We can find the ball's angular speed:
$\omega = \frac{v}{r} = \frac{3.5~cm/s}{2.5~cm} = 1.4~rad/s$
The ball's angular speed is $1.4~rad/s$
