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 = 180 m15 m/sF = ?

A 600 kg car drives around a flat curve of radius 180 m at a constant 15 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 15 m/sr = 180 m
Fc = N
2.Easy
r = 160 m25 m/sac​ = ?

A 1300 kg car drives around a flat curve of radius 160 m at a constant 25 m/s. Find its centripetal acceleration ac.

m = 1300 kgv = 25 m/sr = 160 m
ac = m/s²
3.Medium
r = 65 mvmax​ = ?

A car takes a flat curve of radius 65 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 65 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 110 mvmax​ = ?

A car takes a flat curve of radius 110 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 = 110 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
R = 3.5 mh = 16.45 m

A 1 kg cart is released from rest at a height of 16.45 m on a frictionless track and runs through a vertical loop of radius 3.5 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 = 1 kgh = 16.45 mR = 3.5 mg = 9.81 m/s²
Ntop = N
6.Hard
r = 1.4 m11 m/svtop​ = ?

A 1.9 kg ball on a light string 1.4 m long is swung in a vertical circle. At the lowest point its speed is 11 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.9 kgr = 1.4 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. Fc = 750 N
  2. 2. ac = 3.906 m/s²
  3. 3. vmax = 21.13 m/s
  4. 4. vmax = 23.23 m/s
  5. 5. Ntop = 43.16 N
  6. 6. Ttop = 71.02 N

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