Answer
(a) $3\pi\ rad$
(b) $24\pi\ in$
(c) $\frac{8\pi}{3}\ in/min$
Work Step by Step
Given $r=8\ in, \omega=\frac{\pi}{3}\ rad/min, t=9\ min$, we have:
(a) the angle generated by P in time t is $\theta=\omega t=\frac{\pi}{3}\times9=3\pi\ rad$
(b) the distance traveled by P along the circle in time t is $s=r\theta=24\pi\ in$
(c) the linear speed of P is $v=\omega r=\frac{\pi}{3}\times8=\frac{8\pi}{3}\ in/min$
