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 = 0.2 mv33 rpm

A small object sits 20 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find its centripetal acceleration ac.

n = 33 rpmr = 0.2 m
ac = m/s²
2.Easy
r = ?300 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 300 km/h?

v = 300 km/hamax = 2 m/s²
rmin = m
3.Medium
r = 150 mvmax​ = ?

A car takes a flat curve of radius 150 m. The coefficient of static friction between tyres and road is 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 150 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 100 mvmax​ = ?

A car takes a flat curve of radius 100 m. The coefficient of static friction between tyres and road is 0.4. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 100 mμs = 0.4g = 9.81 m/s²
vmax = m/s
5.Hard
R = 1.5 mh = 6.6 m

A 0.5 kg cart is released from rest at a height of 6.6 m on a frictionless track and runs through a vertical loop of radius 1.5 m. Use g = 9.81 m/s². Find the normal force Nbottom of the track on the cart at the bottom of the loop.

m = 0.5 kgh = 6.6 mR = 1.5 mg = 9.81 m/s²
Nbottom = N
6.Hard
R = 7.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 7.5 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 = 7.5 mv₀ = 0
hmin = m

Answer key

  1. 1. ac = 2.388 m/s²
  2. 2. rmin = 3472 m
  3. 3. vmax = 29.71 m/s
  4. 4. vmax = 19.81 m/s
  5. 5. Nbottom = 48.07 N
  6. 6. hmin = 18.75 m

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