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 = 200 m29 m/sac​ = ?

A 700 kg car drives around a flat curve of radius 200 m at a constant 29 m/s. Find its centripetal acceleration ac.

m = 700 kgv = 29 m/sr = 200 m
ac = m/s²
2.Easy
r = 0.85 mv = ?33 rpm

A small object sits 85 cm from the axis of a disc that turns at a steady 33 revolutions per minute. Find the speed v of the object.

n = 33 rpmr = 0.85 m
v = m/s
3.Medium
r = 1.9 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 1.9 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 1.9 mμs = 0.5g = 9.81 m/s²
ω = rad/s
4.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.6g = 9.81 m/s²
vmax = m/s
5.Hard
R = 4 mh = 14 m

A 4.5 kg cart is released from rest at a height of 14 m on a frictionless track and runs through a vertical loop of radius 4 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 4.5 kgh = 14 mR = 4 mg = 9.81 m/s²
Ntop = N
6.Hard
r = 0.8 mv = 6 m/s

A 0.4 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.4 kgr = 0.8 mv = 6 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. ac = 4.205 m/s²
  2. 2. v = 2.937 m/s
  3. 3. ω = 3.213 rad/s
  4. 4. vmax = 28.71 m/s
  5. 5. Ntop = 88.29 N
  6. 6. T = 21.92 N

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