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 = 190 m25 m/sF = ?

A 1600 kg car drives around a flat curve of radius 190 m at a constant 25 m/s. Find the inward (centripetal) force Fc needed.

m = 1600 kgv = 25 m/sr = 190 m
Fc = N
2.Easy
r = 0.2 mv = ?90 rpm

A small object sits 20 cm from the axis of a disc that turns at a steady 90 revolutions per minute. Find the speed v of the object.

n = 90 rpmr = 0.2 m
v = m/s
3.Medium
r = 115 m26 m/s

A 1300 kg car drives over the top of a hump in the road at 26 m/s. The top of the hump is a circular arc of radius 115 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1300 kgv = 26 m/sr = 115 mg = 9.81 m/s²
N = N
4.Medium
θ = 10°to centrev = ?

A curve of radius 160 m is banked at 10°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 160 mθ = 10°g = 9.81 m/s²
v = m/s
5.Hard
r = 0.9 mv = 5.5 m/s

A 1.7 kg ball on a string 0.9 m long is swung in a vertical circle. At the lowest point it moves at 5.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.7 kgr = 0.9 mv = 5.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1 mv = 6 m/s

A 1.5 kg ball on a string 1 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 = 1.5 kgr = 1 mv = 6 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 5263 N
  2. 2. v = 1.885 m/s
  3. 3. N = 5111 N
  4. 4. v = 16.64 m/s
  5. 5. T = 73.82 N
  6. 6. T = 68.72 N

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