Circular motion worksheet with answers

A 0.5 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 110 N. Find the highest speed v_max the stone can have.

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?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

A car takes a flat curve of radius 65 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 small cart is released from rest on a frictionless track and runs into a vertical loop of radius 10 m. From what minimum height h_min above the bottom of the loop must it start to stay on the track at the top of the loop?

A 2 kg cart is released from rest at a height of 15.4 m on a frictionless track and runs through a vertical loop of radius 5.5 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.