Circular motion worksheet with answers

A 1400 kg car drives around a flat curve of radius 60 m at a constant 17 m/s. Find the inward (centripetal) force F_c needed.

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 small ball on a string of length 1.8 m moves in a horizontal circle so that the string makes a constant angle of 20° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

A small ball on a string of length 1.1 m moves in a horizontal circle so that the string makes a constant angle of 25° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the time T for one revolution.

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 4 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 curve of radius 270 m is banked at 25°, and the coefficient of static friction between tyres and road is 0.25. 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.