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=(192\pi )/(m)\\\\ r=26 \end{cases}\implies v=\cfrac{(192\pi )/(m)}{26} \\\\\\ v=\cfrac{4992\pi }{m}`