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 240 km/h?

A 2 kg stone is whirled in a horizontal circle of radius 2 m on a smooth, level table, held by a string that breaks at a tension of 50 N. Find the highest speed v_max the stone can have.

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.8. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

A car takes a flat curve of radius 55 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 curve of radius 210 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the lowest speed v_min at which a car can take the curve without sliding down the bank.

A ball on a string 1.5 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed v_min at the top for which the string just stays tight?