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 0.8 m/s². What is the smallest radius r_min for a curve taken at 120 km/h?

v = 120 km/ha_max = 0.8 m/s²

r_min = m

2.Easy

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?

v = 250 km/ha_max = 1 m/s²

r_min = m

3.Medium

A car drives over the top of a hump in the road, which is a circular arc of radius 20 m. Use g = 9.81 m/s². Above what speed v_max do the wheels leave the road at the top?

r = 20 mg = 9.81 m/s²

v_max = m/s

4.Medium

A 1300 kg car drives over the top of a hump in the road at 7 m/s. The top of the hump is a circular arc of radius 35 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1300 kgv = 7 m/sr = 35 mg = 9.81 m/s²

N = N

5.Hard

A 0.6 kg ball on a light string 1.5 m long is swung in a vertical circle. At the lowest point its speed is 9 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension T_top in the string at the highest point.

m = 0.6 kgr = 1.5 mv_bottom = 9 m/sg = 9.81 m/s²

T_top = N

6.Hard

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?

r = 1.5 mg = 9.81 m/s²

v_min = m/s

Answer key

1. r_min = 1389 m
2. r_min = 4823 m
3. v_max = 14.01 m/s
4. N = 10933 N
5. T_top = 2.97 N
6. v_min = 3.836 m/s

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