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 worksheetPractise 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
r = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.8 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 0.8 m/s²
rmin = m
2.Easy
r = 100 m10 m/sF = ?

A 1800 kg car drives around a flat curve of radius 100 m at a constant 10 m/s. Find the inward (centripetal) force Fc needed.

m = 1800 kgv = 10 m/sr = 100 m
Fc = N
3.Medium
r = 45 mvmax​ = ?

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 vmax at which the car can take the curve without skidding.

r = 45 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 45 mvmax​ = ?

A car takes a flat curve of radius 45 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 45 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 280 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the lowest speed vmin at which a car can take the curve without sliding down the bank.

r = 280 mθ = 30°μs = 0.4g = 9.81 m/s²
vmin = m/s
6.Hard
r = 1.2 mv = 8 m/s

A 1.3 kg ball on a string 1.2 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.3 kgr = 1.2 mv = 8 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. rmin = 1389 m
  2. 2. Fc = 1800 N
  3. 3. vmax = 18.79 m/s
  4. 4. vmax = 14.86 m/s
  5. 5. vmin = 19.89 m/s
  6. 6. T = 82.09 N

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