Question

Your 64-cmcm-diameter car tire is rotating at 3.8 rev/s when suddenly you press down hard on the accelerator. After traveling 240 mm, the tire's rotation has increased to 6.5 rev/s.

What was the tire's angular acceleration? Give your answer in rad/s2rad/s2.

Express your answer with the appropriate units.

Answer 1

Given the diameter of the car's tire is D=64cm=0.64m.

The radius of the car's tire is

The distance covered by the car in one revolution is equal to the circumference of the tire

The distance covered by the car is 240 meters. The number of revolutions of the car's tire are

Initial angular velocity of the car's tire is

Final angular velocity of the car's tire is

The angular distance covered by the car is

To find the angular acceleration of the car's tire we use the following kinematics equaion

Substituting values

Using we get