How many revolutions per minute are the wheels turning?

Question

The diameter of each wheel of a bicycle is 26 inches. If you are traveling at a speed of 35 miles per hour on this bicycle, through how many revolutions per minute are the wheels turning?

Answer 1

If the diameter is 26 inches, then the circumference is 26Π.  So that's how far the wheel travels in each revolution.  That's about 81.68 inches.

 

How many inches are there in a mile?  12 * 5280, because there are 12 inches in a foot and 5280 feet in a mile.  That's 63360.  If the bike travels at 35 miles per hour, that's 35 * 63360 inches per hour.  That's 2217600.

 

There are 60 minutes in one hour, so divide 2217600 by 60 to get the number of inches traveled in one minute.  That's 36960.

 

So we know the number of inches per minute and we know the number of inches per revolution.  So divide 39360 inches per minute by 81.68 inches per revolution to get the number of revolutions per minute. 

 

That gives 452.5.

 

 

Answer 2

William,

 

Diameter is 26 inches

 

So in 1 revolution distance covered is 26*pi inches

 

Now 1 mile = 63360 inches

 

So 1 revolution = 26*pi/(63360) miles

 

Speed = 35 miles per h  = 35/60 miles/minute

 

Number of revolutions per minute = (35/60)/distance of 1 revolution 

= 35*63360/60*26*pi = 452.5