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

F the diameter is 1/2 mile, that is 0.5 mile, then the radius is 0.25 - half of it!

the angular speed is theta/time, which means

w=theta/time

but another formula for it is Velocity*radians

w=velocity*radians

velocity is 180 mph and radians are (revolution/2 radius), that is:

w=180 * (1/2*0.25)

and if we calculate this, we have: w=114.59, which is the correct answer!