Worksheet: Circular Motion Problems

In this worksheet, we will practice applying rotational kinematics and centripetal dynamics to problems in various situations.


A plumb bob hangs from the roof of a railroad car. The car travels around a circular track of radius 228 m at a speed of 63 km/h. At what angle from the vertical does the plumb bob hang while the car travels around the circular track?


A wind turbine is rotating at 0.500 rev/s and slows to a stop in 10.0 s. Its blades are 20.0 m in length.

What is the angular acceleration of the turbine?

What is the centripetal acceleration of the tip of the blades at 𝑡=0s?


The driver of a car moving at 90.0 km/h presses down on the brake as the car enters a circular curve of radius 150.0 m. If the speed of the car is decreasing at a rate of 9.0 km/h each second, what is the magnitude of the acceleration of the car at the instant its speed is 60.0 km/h?


A car takes a banked curve of radius 100.0 m at an angle of 15.0. If the car takes a banked curve at less than the ideal speed, friction is needed to keep it from sliding toward the inside of the curve (a problem on icy mountain roads).

Calculate the ideal speed for the car to take the curve.

What is the minimum coefficient of friction needed for a frightened driver to take the curve at 20.0 km/h?


A man stands on a merry-go-round that is rotating at 2.5 rad/s. The coefficient of static friction between the man’s shoes and the merry-go-round’s surface is 0.50. How far from the merry-go-round’s axis of rotation can the man stand and continue to be held in place by friction?


A child with mass 40 kg sits on the edge of a merry-go-round at a distance of 3.0 m from its axis of rotation. The merry-go-round accelerates from rest to 0.40 rev/s in 10 s. The coefficient of static friction between the child and the surface of the merry-go-round is 0.60. After the merry-go-round has accelerated for 5.0 seconds, by how much does the frictional force on the child exceed the force accelerating her due to the merry-go-round’s rotation?

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