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A race car is driven around a circular track at a constant speed of 180mph. If the diameter is 1/2 mile, what is the angular speed of the car? Express your answer in revolutions per hour. The formula for angular speed is w=theta (in radians)/time

Verified Answer :

If 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 Velocityradians

w=velocityradians

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

w=180(1/2\(\pi\)0.25)
and if we calculate this, we have: w=114.59, which is the correct answer!

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