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

A 1600 kg car drives around a flat curve of radius 190 m at a constant 23 m/s. Find the inward (centripetal) force F_c needed.

m = 1600 kgv = 23 m/sr = 190 m

F_c = N

2.Easy

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 160 km/h?

v = 160 km/ha_max = 2 m/s²

r_min = m

3.Medium

A car takes a flat curve of radius 75 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 = 75 mμ_s = 0.6g = 9.81 m/s²

v_max = m/s

4.Medium

A road engineer wants cars to take a curve of radius 320 m at 70 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 320 mv = 70 km/hg = 9.81 m/s²

θ = °

5.Hard

A curve of radius 140 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.15. 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 = 140 mθ = 15°μ_s = 0.15g = 9.81 m/s²

v_max = m/s

6.Hard

A curve of radius 230 m is banked at 20°, and the coefficient of static friction between tyres and road is 0.3. 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 = 230 mθ = 20°μ_s = 0.3g = 9.81 m/s²

v_max = m/s

Answer key

1. F_c = 4455 N
2. r_min = 987.7 m
3. v_max = 21.01 m/s
4. θ = 6.868 °
5. v_max = 24.46 m/s
6. v_max = 41.01 m/s

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