Circular motion worksheet with answers

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius r_min for a curve taken at 250 km/h?

A 1.8 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 70 N. Find the highest speed v_max the stone can have.

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 8.5 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 0.4 kg ball on a light string 0.8 m long is swung in a vertical circle. At the lowest point its speed is 6.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.