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 = 90 m21 m/sac​ = ?

A 1200 kg car drives around a flat curve of radius 90 m at a constant 21 m/s. Find its centripetal acceleration ac.

m = 1200 kgv = 21 m/sr = 90 m
ac = m/s²
2.Easy
r = 30 m18 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 30 m at a constant 18 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 18 m/sr = 30 m
ac = m/s²
3.Medium
r = 55 mvmax​ = ?

A car takes a flat curve of radius 55 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 = 55 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 2.1 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.1 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.6. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 2.1 mμs = 0.6g = 9.81 m/s²
ω = rad/s
5.Hard
r = 0.9 mv = 8 m/s

A 1.8 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 8 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.8 kgr = 0.9 mv = 8 m/sg = 9.81 m/s²
T = N
6.Hard
R = 7 mh = 21 m

A 2.5 kg cart is released from rest at a height of 21 m on a frictionless track and runs through a vertical loop of radius 7 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 = 2.5 kgh = 21 mR = 7 mg = 9.81 m/s²
Nbottom = N

Answer key

  1. 1. ac = 4.9 m/s²
  2. 2. ac = 10.8 m/s²
  3. 3. vmax = 16.42 m/s
  4. 4. ω = 2.79 rad/s
  5. 5. T = 145.7 N
  6. 6. Nbottom = 171.7 N

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