Answer
(a) $\frac{2\pi}{3}\ rad.$
(b) $40\pi\ cm$
(c) $5\pi\ cm/sec$
Work Step by Step
Given $r=60\ cm, \omega=\frac{\pi}{12}\ rad/sec$, we have:
(a) The angle generated by P in 8 sec. is given by $\theta = \omega t=\frac{\pi}{12}(8)=\frac{2\pi}{3}\ rad.$
(b) The distance traveled by P along the circle in 8 sec. is given by $s=r\cdot\theta=60(\frac{2\pi}{3})=40\pi\ cm$
(c) The linear speed of P is given by $v=r\omega=60(\frac{\pi}{12})=5\pi\ cm/sec$
