Circular motion worksheet with answers

Free printable Circular motion worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

New worksheet Practise online with hints

For teachers: free to print, copy and use in class. Every new worksheet has new values and its own answer key. A link to ExamProblems on your course page is appreciated.

Name: ____________________ Date: ____________

1.Easy

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius r_min for a curve taken at 300 km/h?

v = 300 km/ha_max = 0.5 m/s²

r_min = m

2.Easy

An 800 kg car drives around a flat curve of radius 170 m at a constant 25 m/s. Find its centripetal acceleration a_c.

m = 800 kgv = 25 m/sr = 170 m

a_c = m/s²

3.Medium

A car takes a flat curve of radius 30 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed v_max at which the car can take the curve without skidding.

r = 30 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

4.Medium

A car takes a flat curve of radius 45 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.

r = 45 mμ_s = 0.4g = 9.81 m/s²

v_max = m/s

5.Hard

A ball on a string 1 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?

r = 1 mg = 9.81 m/s²

v_min = m/s

6.Hard

A curve of radius 60 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.1. Use g = 9.81 m/s². Find the highest speed v_max at which a car can take the curve without sliding up and out.

r = 60 mθ = 15°μ_s = 0.1g = 9.81 m/s²

v_max = m/s

Answer key

1. r_min = 13889 m
2. a_c = 3.676 m/s²
3. v_max = 13.29 m/s
4. v_max = 13.29 m/s
5. v_min = 3.132 m/s
6. v_max = 14.92 m/s

Full step-by-step solutions: practise this topic on examproblems.com.