Chapter 3 - Radian Measure and the Unit Circle - Section 3.4 Linear and Angular Speed - 3.4 Exercises - Page 130: 10

(a) $40\pi\,rad$ (b) $480\pi \,ft$ (c) $96\pi\,ft/min$

(a) $\omega=\frac{\theta}{t}$ $\implies \theta=\omega t=(8\pi\,rad/min)\times5\,min$ $=40\pi\,rad$ (b) Using the arc length formula,we have Distance traveled $s=r\theta= (12\,ft)(40\pi)$ $=480\pi \,ft$ (c) Linear speed $v=r\omega$ $=12\,ft(8\pi\,rad/min)=96\pi\,ft/min$