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
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 Velocity*radians w=velocity*radians velocity is 180 mph and radians are (revolution/2[latex] \pi [/latex] radius), that is: w=180*(1/2[latex] \pi [/latex]*0.25) and if we calculate this, we have: w=114.59, which is the correct answer!