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 = 170 m20 m/sF = ?

A 1400 kg car drives around a flat curve of radius 170 m at a constant 20 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 20 m/sr = 170 m
Fc = N
2.Easy
r = 0.6 mv = ?78 rpm

A small object sits 60 cm from the axis of a disc that turns at a steady 78 revolutions per minute. Find the speed v of the object.

n = 78 rpmr = 0.6 m
v = m/s
3.Medium
θ = 15°to centrev = ?

A curve of radius 390 m is banked at 15°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 390 mθ = 15°g = 9.81 m/s²
v = m/s
4.Medium
r = 130 mvmax​ = ?

A car takes a flat curve of radius 130 m. The coefficient of static friction between tyres and road is 0.3. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 130 mμs = 0.3g = 9.81 m/s²
vmax = m/s
5.Hard
r = 1.4 mv = 3 m/s

A 1 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 3 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.4 mv = 3 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.6 mv = 7 m/s

A 1.1 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 7 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.1 kgr = 0.6 mv = 7 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 3294 N
  2. 2. v = 4.901 m/s
  3. 3. v = 32.02 m/s
  4. 4. vmax = 19.56 m/s
  5. 5. T = 16.24 N
  6. 6. T = 100.6 N

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