Circular motion worksheet with answers

A small object sits 15 cm from the axis of a disc that turns at a steady 120 revolutions per minute. Find its centripetal acceleration a_c.

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

An 800 kg car drives over the top of a hump in the road at 7 m/s. The top of the hump is a circular arc of radius 20 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

A car takes a flat curve of radius 80 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

A 1.1 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

A 4 kg cart is released from rest at a height of 38.7 m on a frictionless track and runs through a vertical loop of radius 9 m. Use g = 9.81 m/s². Find the normal force N_bottom of the track on the cart at the bottom of the loop.