Answer
(a) $3\pi\,rad$
(b) $24\,\pi\,inches$
(c) $\frac{8\pi}{3}\,in/min$
Work Step by Step
(a) $\omega=\frac{\theta}{t}$
$\implies \theta=\omega t=(\frac{\pi}{3}\,rad/min)\times9\,min$
$=3\pi\,rad$
(b) Using the arc length formula,we have
Distance traveled $s=r\theta= (8\,in)(3\pi)$
$=24\pi \,inches$
(c) Linear speed $v=r\omega$
$=8\,in(\frac{\pi}{3}\,rad/min)=\frac{8\pi}{3}\,in/min$
