Trigonometry question?

Question

a car with a wheel of radius 14 inches is moving with a speed of 55 mph. find the angular speed of the wheel in radians per second.

i need help on how to get to the answer. like how do i convert from 55mph to radians per second. and how do i put it in the formula?

Answer 1

1 mile = 5280 ft. = 5280*12 inches = 63360 inches
So: 55 mph = 55 miles/hr
= 55*63360 inches/3600s
= 968 inches/sec
The circumference of the wheel is 2*π*14 (inches). Thus the wheel's rotation speed is:
968 (inches/sec) / {2*π*14 (inches)}
= 968 / {2*π*14} (round/sec)
But one round is of 2*π in radians. Hence Thus the wheel's rotation speed is:
968 / {2*π*14} (round/sec)
= 2*π*968 / {2*π*14} (/sec)
= 968 /14 (/sec)
= 69.14 (radians)/sec
or simply: 69.14 /sec