Circular motion worksheet with answers

A small object sits 140 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration a_c.

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

A car takes a flat curve of radius 25 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

A 2 kg cart is released from rest at a height of 32 m on a frictionless track and runs through a vertical loop of radius 10 m. Use g = 9.81 m/s². Find the normal force N_top of the track on the cart at the top of the loop.

A 2 kg cart is released from rest at a height of 15 m on a frictionless track and runs through a vertical loop of radius 5 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.