Question

A cyclist is riding a bicycle whose wheels have a diameter of 1.8 feet. Suppose the wheels turn at a rate of 240 revolutions

per minute.
(a) Find the angular speed of the wheels in radians per minute.
(b) Find the speed of the cyclist in feet per minute.
Do not round any intermediate computations, and round your answer to the nearest whole number

Answer 1

well, one revolution is 2π radians, so 240 revolutions/min will just be

`\cfrac{240~~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{min}\cdot \cfrac{2\pi }{~~\begin{matrix} r \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{480\pi}{min}\implies 480\pi (rad)/(min)`

well, v = rω, and since we know ω from above, so

`\omega=\cfrac{480\pi}{min}\qquad \qquad v=\left( \cfrac{1.8}{2}ft \right) \left( \cfrac{480\pi}{min} \right)\implies v=\cfrac{432\pi~ft}{min} \implies v\approx 1357(ft)/(min)`