[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]
