Question

A race car is driven around a circular tract at a constant speed of 180 miles per hour. If the diameter of the track is 1/2 miles, what is the angular speed of the car? Express your answer in revolutions per hour.

I know the answer is 114.59 revolutions per hour, but I don't know what steps to take to get to that answer. Please show me.

Thanks.

the arclength a of a circle is given by a=rθ where θ is in radians.

differentiate with respect to t
da/dt = .25dθ/dt
180 = .25dθ/dt
dθ/dt = 720 radians per hour

one revolution is 2pi radians, so divide 720 by 2pi to get 114.59 revolutions.

Answer 1

Therefore, the angular speed of the car is 114.59 revolutions per hour.