Question

What is the angular speed and the number of revolutions per hour

Answer 1

`\begin{gathered} r=(64ft)/(2)=32ft \\ v=7(mi)/(hour)\cdot\frac{5280ft}{1\text{ mi}}\cdot\frac{1hour}{60\text{ minutes}}=616\text{ ft/min} \\ To\text{ find }angulat\text{ sp}eed \\ v=wr \\ \text{Solving w} \\ w=(v)/(r)=\frac{616\text{ ft/min}}{32ft}=19\text{ rad/min} \\ \text{The angular spe}ed\text{ is }19\text{ rad/min} \\ \\ To\text{ find revolution per hour } \\ 19(rad)/(\min)\cdot(60\min)/(1hour)\cdot(1rev)/(2\pi rad)=153\text{ rev/hour} \\ \text{The whe}el\text{ }makes\text{ }153\text{ rev/hour} \end{gathered}`