Circular motion worksheet with answers

A 1400 kg car drives around a flat curve of radius 60 m at a constant 25 m/s. Find its centripetal acceleration a_c.

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.2 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

A 1100 kg car drives over the top of a hump in the road at 9 m/s. The top of the hump is a circular arc of radius 85 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

A car takes a flat curve of radius 45 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

A 1.4 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 3.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

A 0.6 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.