Posted by **michelle** on Tuesday, May 1, 2007 at 10:41pm.

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 this Question

## Related Questions

Trigonometry - A race car is driven around a circular track at a constant speed...

Trigonometry - A race car is driven around a circular track at a constant speed ...

math - ANGULAR SPEED OF A RACE CAR. A race car is driven around a circular track...

Math - A small truck is to be driven 300 miles on a freeway at a constant speed ...

maths - A motorist travels 120 miles to his destionation at an average speed of ...

Math - Two cars run at constant speeds around a one-mile racetrack. If the cars ...

College Physics - The Daytona 500 stock car race is held on a circular track ...

PHY SCI - A race car goes around a circular, level track with a diameter of 1.00...

algebra - Rachel allows herself 1 hour to reach a sale appointment 50 mile s ...

trig - A car travels around a circular track at 185 miles per hour. Is this a ...