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.

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

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