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 = 170 m12 m/sac​ = ?

A 1500 kg car drives around a flat curve of radius 170 m at a constant 12 m/s. Find its centripetal acceleration ac.

m = 1500 kgv = 12 m/sr = 170 m
ac = m/s²
2.Easy
r = 130 m20 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 130 m at a constant 20 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 20 m/sr = 130 m
ac = m/s²
3.Medium
r = 3.6 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.6 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.3. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 3.6 mμs = 0.3g = 9.81 m/s²
n = rpm
4.Medium
r = 30 mvmax​ = ?

A car drives over the top of a hump in the road, which is a circular arc of radius 30 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?

r = 30 mg = 9.81 m/s²
vmax = m/s
5.Hard
r = 1 mv = 8.5 m/s

A 2 kg ball on a string 1 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 2 kgr = 1 mv = 8.5 m/sg = 9.81 m/s²
T = N
6.Hard
θ = 8°to centrevmax​ = ?

A curve of radius 140 m is banked at 8°, 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 = 140 mθ = 8°μs = 0.25g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. ac = 0.8471 m/s²
  2. 2. ac = 3.077 m/s²
  3. 3. n = 28.78 rpm
  4. 4. vmax = 17.16 m/s
  5. 5. T = 164.1 N
  6. 6. vmax = 23.58 m/s

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