Angular Speed: A moving car?

Question

A car is moving at the rate of 50 miles per hour, and the diameter of its wheel is 2.5 feet.

A) Find the number of revolutions per minute that the wheels are rotating.

B) Find the angular speed of the wheels in radians per minute.

Answer 1

50 miles / hour * hour / 60 min * 5280 ft / mile =  4400 feet / min

so the wheel must cover 4400 feet / min

if the diameter is 2.5 feet, then the radius is 2.5 / 2 = 1.25 feet

circumference of wheel = 2 pi r = 2 pi (2.5 feet/2) = 2.5 pi feet / rev

4400 feet / min * rev / (2.5 pi) feet = 560.2 rpm for the wheels

B)  since one revolution covers one circumference, then there are 2pi radians / revolution

560.2 rev / min * 2pi radians / rev = 1120.5pi radians / min , or 3520 radians / min