Circular motion worksheet with answers

A 1.9 kg stone is whirled in a horizontal circle of radius 1.1 m on a smooth, level table, held by a string that breaks at a tension of 30 N. Find the highest speed v_max the stone can have.

A 1100 kg car drives around a flat curve of radius 20 m at a constant 17 m/s. Find its centripetal acceleration a_c.

A car takes a flat curve of radius 85 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.

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.5 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. 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 6.5 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 0.3 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.