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.

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17-07-2017
Mathematics

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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.

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jdoe0001 jdoe0001 · Answer 1 · 2017-07-17T22:43:22+02:00

[tex]\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}[/tex]