Circular motion worksheet with answers

A 900 kg car drives around a flat curve of radius 130 m at a constant 15 m/s. Find its centripetal acceleration a_c.

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 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 3.4 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 car takes a flat curve of radius 145 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

A 1.5 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

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?