Question

Please help. WILL MEDAL! The wheel was rolling along at 30 radians per second. What was its linear velocity in miles per hour if the radius was 6 meters? @mathstudent55 @satellite73 @jim_thompson5910 @nincompoop @jigglypuff314 @sleepyjess @zepdrix @Zarkon @iPwnBunnies

Answer 1

\[\frac{ 30 rad }{ 1 \sec }\]

Answer 2

\(\omega = 30 ~\dfrac{rad}{sec} \)

\(v = r\omega \)

Answer 3

\(r = 6 ~m\)

Answer 4

v = velocity?
r = radius?

Answer 5

Use the formula for linear velocity with your given info.
Then convert units.

Answer 6

Yes.

\(\omega\) = angular velocity

\(v\) = linear velicity

\(r\) = radius

Answer 7

^velocity

Answer 8

Sorry, but gtg.
You're in good hands with Jim writing something.

Answer 9

\[v = 6m (\frac{ 30 rad }{ \sec })\]

Answer 10

Start with
\[\Large \frac{ 30 \text{ rad} }{ 1 \text{ sec} }\]

Then multiply by the conversion factor (C meters/2pi radians)

\[\Large \frac{ 30 \text{ rad} }{ 1 \text{ sec} } \times \frac{ C \text{ meters} }{ 2\pi \text{ rad} }\]

where C is the circumference of the circle


Notice how the radian units cancel. This leaves just the units "meters" and "seconds"


\[\Large \frac{ 30 {\color{red}{\cancel{{\color{black}{\text{ rad}}}}} }}{ 1 \text{ sec} } \times \frac{ C \text{ meters} }{ 2\pi {\color{red}{\cancel{{\color{black}{\text{ rad}}}}} }}\]

Answer 11

Then you'll use conversion factors to go from meters/second to miles/hour

Answer 12

\[\frac{ 64800000 }{ 321868.8\pi }\frac{ mi }{ hr }\]

Answer 13

I'm not sure how you have pi in your answer. The pi terms should cancel. I would leave C in terms of pi then allow the pi terms to cancel.