Question

A car is moving at a rate of 65 miles per hour and the diameter of its wheels is 2 feet.
a) Find the number of revolutions per minute the wheels are rotating.
b) Find the angular speed of the wheels in radians per minute.

Answer 1

a) 910.37 rpm
b) 5720 radians per minute.

First, figure out how many feet per hour the car is moving.
65 * 5280 = 343200

Now figure out how many feet per minute the car is moving
343299 / 60 = 5720

Figure out the circumference of the tires in feet.
2 * pi = 2 * 3.1415926535...  = 6.283185

Divide the distance traveled by the circumference of the wheels
5720 / 6.283185 = 910.3663 rpm. Rounded to 2 decimal places is 910.37

There is 2 pi radians in a circle. So to convert from RPM, just multiply by 2*pi. So
910.37 * 2 * pi = 5720

Answer 2

a) 910.83 b) 1821.66 When a wheel makes 1 revolution, the car will move forward by an amount equal to the wheel's circumference. We were given the wheel's diameter; it's radius is half that, and... C = 2 * pi * r = 2 * pi * ( 2 feet / 2 ) = 2 * pi feet The car moves at 65 miles per hour. There are 5280 feet in a mile. The number of revolutions in an hour is the distance traveled divided by the wheel's circumference: revs/hr = 65 * 5280 / C = 343200 / (2 * pi ) = 54,649.68 The number of revolutions per minute is this divided by 60 because there are 60 minutes in one hour. revs/min = 54,649.68 / 60 = 910.83 There are 2 radians in a circle, so radians per minute = 2 * revs/min = 1821.66