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 = 1.3 mv60 rpm

A small object sits 130 cm from the axis of a disc that turns at a steady 60 revolutions per minute. Find its centripetal acceleration ac.

n = 60 rpmr = 1.3 m
ac = m/s²
2.Easy
r = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 0.5 m/s²
rmin = m
3.Medium
r = 3.9 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.4. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.9 mμs = 0.4g = 9.81 m/s²
ω = rad/s
4.Medium
r = 135 mvmax​ = ?

A car takes a flat curve of radius 135 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 135 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
θ = 30°to centrevmin​ = ?

A curve of radius 110 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.3. 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 = 110 mθ = 30°μs = 0.3g = 9.81 m/s²
vmin = m/s
6.Hard
R = 5.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 5.5 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 = 5.5 mv₀ = 0
hmin = m

Answer key

  1. 1. ac = 51.32 m/s²
  2. 2. rmin = 13889 m
  3. 3. ω = 2.508 rad/s
  4. 4. vmax = 19.93 m/s
  5. 5. vmin = 15.97 m/s
  6. 6. hmin = 13.75 m

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