A bicycle wheel is 9 inches in radius. The bicycle is travelling at miles per hour, what is the angular velocity, in revolutions per minute, of the wheel?

Question

tkhunny · Answer

You'll need an actual number in there for the speed.

anonymous · Answer

Oops I left out the 25mph.

tkhunny · Answer

What's the circumference?

anonymous · Answer

Um.. 56.52?

tkhunny · Answer

$2*\pi*9 = 56.55$  Not sure where you were rounding, but it was plenty short.

anonymous · Answer

Okay

tkhunny · Answer

Okay, now it's conversion time.

$\dfrac{25\;mile}{1\;hour}\cdot\dfrac{1\;Rev}{18\pi\;inch}$

What does that do for us?

anonymous · Answer

Converts it into revs.. What we need.

tkhunny · Answer

Good.  Except we need RP(MINUTE).  What else do we need in there?

anonymous · Answer

Minutes

tkhunny · Answer

Well, yes, but how shall it be introduced?

anonymous · Answer

Mm.. No clue.

tkhunny · Answer

How about $\dfrac{1\;hour}{60\;min}$?

anonymous · Answer

Oh yeah.. Then what would be the next step? 1min over..

tkhunny · Answer

You have hours in the denominator originally.  In the new factor, hours need to be in the numerator to get rid of it.

$\dfrac{25\;mile}{1\;hour}\cdot\dfrac{1\;Rev}{18\pi\;inch}\cdot\dfrac{1\;hour}{60\;min}$

Is that something we can work with, or shall we do something about those mismatched linear measurements.  Miles vs. inches?  They are a little off.

tkhunny · Answer

25 miles = 25 * 5280 ft = 25 * 5280 * 12 in

Are we looking familiar?