Respuesta :

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]

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