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 m21 m/sac​ = ?

A 1600 kg car drives around a flat curve of radius 120 m at a constant 21 m/s. Find its centripetal acceleration ac.

m = 1600 kgv = 21 m/sr = 120 m
ac = m/s²
2.Easy
r = 150 m29 m/sac​ = ?

A 1800 kg car drives around a flat curve of radius 150 m at a constant 29 m/s. Find its centripetal acceleration ac.

m = 1800 kgv = 29 m/sr = 150 m
ac = m/s²
3.Medium
θ = ?to centre90 km/h

A road engineer wants cars to take a curve of radius 80 m at 90 km/h without relying on friction. Use g = 9.81 m/s². Find the banking angle θ.

r = 80 mv = 90 km/hg = 9.81 m/s²
θ = °
4.Medium
r = 90 mvmax​ = ?

A car takes a flat curve of radius 90 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 = 90 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
R = 6.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 6.5 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 6.5 mv₀ = 0
hmin = m
6.Hard
r = 0.7 mv = ?

A ball on a string 0.7 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 = 0.7 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 3.675 m/s²
  2. 2. ac = 5.607 m/s²
  3. 3. θ = 38.53 °
  4. 4. vmax = 21.01 m/s
  5. 5. hmin = 16.25 m
  6. 6. vmin = 2.62 m/s

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