A truck with 26-inch diameter wheels is traveling at 65 mi/h. Find the angular speed of the wheels in radians per minute.

Question

A truck with 26-inch diameter wheels is traveling at 65 mi/h. Find the angular speed of the wheels in radians per minute.

How many revolutions per minute do the wheels make? 

Answer 1

A radian is the length of the radius, which is 13 inches.

65 mi/hr is 1 1/12, or 13/12, miles per minute. 13/12 miles in inches is 13/12 x 5280 x 12 = 68,640 inches. Divide that by 13 to get the radians. That gives 5280 radians per minute.

There are 2π radians per revolution. So divides 5280 by 2π to get 840.33809953... which you can round to 840 revolutions per minute.