Question

If a wheel with a radius of 80 inches spins at a rate of 50 revolutions per minute, find the approximate linear velocity in miles per hour.

Answer 1

$\bf \textit{arc's length}\\\\ s=rw\qquad \begin{cases} r=radius\\ w=\textit{angular speed} \end{cases}\qquad w=\cfrac{50 rev}{min}\cdot \cfrac{2\pi }{rev} \\\\\\ w=\cfrac{100\pi }{min}\qquad s=80in\cdot \cfrac{100\pi }{min}\implies s=\cfrac{8000\pi\ in}{min}\\\\ -------------------------------\\\\ \textit{now to convert it to miles/hr} \\\\\\ \cfrac{8000\pi\ in}{min}\cdot \cfrac{ft}{12in}\cdot \cfrac{mile}{5280ft}\cdot \cfrac{60min}{hr}\implies \cfrac{8000\pi \cdot 60\ in}{12\cdot 5280\ hr}$