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.

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1.Easy
r = 1.35 mv90 rpm

A small object sits 135 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find its centripetal acceleration ac.

n = 90 rpmr = 1.35 m
ac = m/s²
2.Easy
r = 200 m25 m/sF = ?

A 600 kg car drives around a flat curve of radius 200 m at a constant 25 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 25 m/sr = 200 m
Fc = N
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 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 150 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 3.5 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.5 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 rotation rate n in revolutions per minute.

r = 3.5 mμs = 0.7g = 9.81 m/s²
n = rpm
5.Hard
R = 6 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 6 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 mv₀ = 0
hmin = m
6.Hard
r = 1.1 mv = ?

A ball on a string 1.1 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 = 1.1 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 119.9 m/s²
  2. 2. Fc = 1875 N
  3. 3. vmax = 27.12 m/s
  4. 4. n = 19.11 rpm
  5. 5. hmin = 15 m
  6. 6. vmin = 3.285 m/s

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