13)
there are 2π radians in 1 revolution, and there are 60 seconds in 1 minute, so keeping that in mind, then,
[tex]\bf \cfrac{4\underline{\pi} }{5~\underline{s}}\cdot \cfrac{rev}{2\underline{\pi} }\cdot \cfrac{60~\underline{s}}{min}\implies \cfrac{4\cdot 60~rev}{5\cdot 2~min}\implies \cfrac{240~rev}{10~min}\implies 24\frac{rev}{min}[/tex]
14)
[tex]\bf \textit{linear velocity}\\\\
v=rw\quad
\begin{cases}
r=radius\\
w=angular~speed\\
----------\\
v=32\frac{m}{sec}\\
w=100\frac{rev}{min}
\end{cases}\\\\
-------------------------------\\\\
\textit{let's convert \underline{w} to }\frac{radians}{sec}[/tex]
[tex]\bf \cfrac{100~\underline{rev}}{\underline{min}}\cdot \cfrac{2\pi }{\underline{rev}}\cdot \cfrac{\underline{min}}{60~sec}\implies \cfrac{100\cdot 2\pi }{60~sec}\implies \cfrac{10\pi }{3~sec}\implies \cfrac{10\pi }{3}\frac{radians}{sec}\\\\
-------------------------------\\\\
v=rw\implies \cfrac{v}{w}=r\implies \cfrac{\frac{30~m}{sec}}{\frac{10\pi }{3~sec}}\implies r=\cfrac{30~m}{\underline{sec}}\cdot \cfrac{3~\underline{sec}}{10\pi }
\\\\\\
r=\cfrac{90}{10\pi }m[/tex]
15)
what is the radians per seconds "w" in revolutions per minute? just another conversion like in 13)
[tex]\bf \cfrac{\underline{\pi} }{3~\underline{sec}}\cdot \cfrac{rev}{2\underline{\pi }}\cdot \cfrac{60~\underline{sec}}{min}\implies \cfrac{60 ~rev}{3\cdot 2 ~min}\implies \cfrac{60 ~rev}{6 ~min}\implies 10\frac{rev}{min}[/tex]
