Expert: Paul Klarreich - 3/5/2007

Question
Paul,
   I am stuck and have no place to turn, need help!!!!
I am working on the current problem...
I have a bike tire with a radius of 13inch turning at a rate 200 revolutions per minute.  How can I figure out how fast the bike is going in MPH?  
I know I have to somehow use the conversion of 5280 feet = 1 mile and that 1 full revolution (360 Degrees) = 2Pi.  I tried using the v = rw equation, but I get very confused, very quickly.  Any and all help would be appreciated.  

Arthur.
P.S. I asked my instructor for help, he gave me the answer which is 15.5mph.  I don't know how to get the answer though!!! AAAHHHH!!!!!!!!

Answer
Questioner:   Arthur
Category:  Advanced Math
 
Subject:  Circular Functions - PreCalc
Question:  Paul,
  I am stuck and have no place to turn, need help!!!!
I am working on the current problem...
I have a bike tire with a radius of 13inch turning at a rate 200 revolutions per minute.  How can I figure out how fast the bike is going in MPH?  
I know I have to somehow use the conversion of 5280 feet = 1 mile and that 1 full revolution (360 Degrees) = 2Pi.  I tried using the v = rw equation, but I get very confused, very quickly.  Any and all help would be appreciated.  

Arthur.
P.S. I asked my instructor for help, he gave me the answer which is 15.5mph.  I don't know how to get the answer though!!! AAAHHHH!!!!!!!!
........................................
Hi, Arthur,

Assuming the 'external' radius of the bike is 13 inches and stays round because it has enough air pressure, the circumference is  2 pi(13) = 26pi inches.

That is how far the bike will go for each revolution of the wheel.

Then 200 RPM --> 200(26pi) inches per minute, or
--> 200(26pi)(60) inches per hour, or
200(26pi)(60)/12  feet per hour, or
200(26pi)(60)/(12*5280) miles per hour.

My calculator gives 15.46996382449519397727816817524 miles per hour.  Close enough.