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 = 1 mvmax​ = ?

A 1.2 kg stone is whirled in a horizontal circle of radius 1 m on a smooth, level table, held by a string that breaks at a tension of 140 N. Find the highest speed vmax the stone can have.

m = 1.2 kgr = 1 mTmax = 140 N
vmax = m/s
2.Easy
r = 180 m10 m/sac​ = ?

A 700 kg car drives around a flat curve of radius 180 m at a constant 10 m/s. Find its centripetal acceleration ac.

m = 700 kgv = 10 m/sr = 180 m
ac = m/s²
3.Medium
L = 0.9 m30°

A small ball on a string of length 0.9 m moves in a horizontal circle so that the string makes a constant angle of 30° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 0.9 mθ = 30°g = 9.81 m/s²
v = m/s
4.Medium
r = 150 mvmax​ = ?

A car takes a flat curve of radius 150 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 = 150 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 15°to centrevmax​ = ?

A curve of radius 130 m is banked at 15°, and the coefficient of static friction between tyres and road is 0.25. Use g = 9.81 m/s². Find the highest speed vmax at which a car can take the curve without sliding up and out.

r = 130 mθ = 15°μs = 0.25g = 9.81 m/s²
vmax = m/s
6.Hard
r = 1 mv = ?

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 vmin at the top for which the string just stays tight?

r = 1 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. vmax = 10.8 m/s
  2. 2. ac = 0.5556 m/s²
  3. 3. v = 1.596 m/s
  4. 4. vmax = 27.12 m/s
  5. 5. vmax = 26.61 m/s
  6. 6. vmin = 3.132 m/s

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