posted by michelle .
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.
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.