Types of Acceleration in Rotation Practice Problems

A toy car of mass 250 g is rolling on a circular vertical loop of diameter 1.0 m. The friction between the car and the loop is 0.45. At the top of the loop, the speed of the car is 0.25 m/s. Determine the magnitude of the tangential acceleration at the top of the loop.

A physics student launches a ball with an initial angular speed of 85.0 rpm on a flat circular path. The radius of the path is 35 cm. The ball is subject to rolling friction. Calculate the time it will take the ball to come to rest. The coefficient of rolling friction is 0.25.

The speed of a particle rotating in a circle of radius 0.5 m is increased from rest at a constant rate of 0.25 m/s². At time t, the magnitude of the centripetal acceleration equals the magnitude of the tangential acceleration. Determine the time t.