Circular motion worksheet with answers

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1.5 m/s². What is the smallest radius r_min for a curve taken at 160 km/h?

A small object sits 75 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find its centripetal acceleration a_c.

A car drives over the top of a hump in the road, which is a circular arc of radius 80 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

A car takes a flat curve of radius 90 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 0.4 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 5.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

A 1.1 kg ball on a light string 1.3 m long is swung in a vertical circle. At the lowest point its speed is 11.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.