Question

14. At what speed in miles per hour will a bicycle travel if the rider can cause the 26-inch diameter wheel to rotate 90 revolutions per minute? Round answer to the nearest tenth.

Answer 1

so    a revolution is just another way to say 2π, so 96 revolutions will then be 96 * 2π, or 192π, so that means the angular speed = w 192 π/m

$\bf v=rw\qquad \begin{cases} w=\textit{angular speed}\\ r=radius\\ v=\textit{linear speed}\\ ----------\\ w=\frac{192\pi }{m}\\\\ r=26 \end{cases}\implies v=\cfrac{\frac{192\pi }{m}}{26} \\\\\\ v=\cfrac{4992\pi }{m}$