Question

Please help me with precalculus??
linear and angular speed

Answer 1

13)

there are 2π radians in 1 revolution, and there are 60 seconds in 1 minute, so keeping that in mind, then,


`\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(rev)/(min)`

14)


`\bf \textit{linear velocity}\\\\ v=rw\quad \begin{cases} r=radius\\ w=angular~speed\\ ----------\\ v=32(m)/(sec)\\ w=100(rev)/(min) \end{cases}\\\\ -------------------------------\\\\ \textit{let's convert \underline{w} to }(radians)/(sec)`


`\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}(radians)/(sec)\\\\ -------------------------------\\\\ v=rw\implies \cfrac{v}{w}=r\implies \cfrac{(30~m)/(sec)}{(10\pi )/(3~sec)}\implies r=\cfrac{30~m}{\underline{sec}}\cdot \cfrac{3~\underline{sec}}{10\pi } \\\\\\ r=\cfrac{90}{10\pi }m`

15)

what is the radians per seconds "w" in revolutions per minute? just another conversion like in 13)


`\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(rev)/(min)`