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 m11 m/sF = ?

A 1200 kg car drives around a flat curve of radius 170 m at a constant 11 m/s. Find the inward (centripetal) force Fc needed.

m = 1200 kgv = 11 m/sr = 170 m
Fc = N
2.Easy
r = 1.05 mv90 rpm

A small object sits 105 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find its centripetal acceleration ac.

n = 90 rpmr = 1.05 m
ac = m/s²
3.Medium
L = 1.2 m15°

A small ball on a string of length 1.2 m moves in a horizontal circle so that the string makes a constant angle of 15° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.2 mθ = 15°g = 9.81 m/s²
v = m/s
4.Medium
r = 3.1 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.1 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.1 mμs = 0.7g = 9.81 m/s²
ω = rad/s
5.Hard
θ = 30°to centrevmax​ = ?

A curve of radius 270 m is banked at 30°, and the coefficient of static friction between tyres and road is 0.1. 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 = 270 mθ = 30°μs = 0.1g = 9.81 m/s²
vmax = m/s
6.Hard
θ = 10°to centrevmax​ = ?

A curve of radius 180 m is banked at 10°, and 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 a car can take the curve without sliding up and out.

r = 180 mθ = 10°μs = 0.3g = 9.81 m/s²
vmax = m/s

Answer key

  1. 1. Fc = 854.1 N
  2. 2. ac = 93.27 m/s²
  3. 3. v = 0.9035 m/s
  4. 4. ω = 2.126 rad/s
  5. 5. vmax = 43.64 m/s
  6. 6. vmax = 29.8 m/s

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