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 = 40 m21 m/sF = ?

A 1300 kg car drives around a flat curve of radius 40 m at a constant 21 m/s. Find the inward (centripetal) force Fc needed.

m = 1300 kgv = 21 m/sr = 40 m
Fc = N
2.Easy
r = 130 m10 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 130 m at a constant 10 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 10 m/sr = 130 m
ac = m/s²
3.Medium
r = 20 mvmax​ = ?

A car drives over the top of a hump in the road, which is a circular arc of radius 20 m. Use g = 9.81 m/s². Above what speed vmax do the wheels leave the road at the top?

r = 20 mg = 9.81 m/s²
vmax = m/s
4.Medium
θ = 12°to centrev = ?

A curve of radius 150 m is banked at 12°. At what speed v can a car take it with no friction needed at all? Use g = 9.81 m/s².

r = 150 mθ = 12°g = 9.81 m/s²
v = m/s
5.Hard
r = 0.9 m8.5 m/svtop​ = ?

A 1.6 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 8.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.6 kgr = 0.9 mvbottom = 8.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1.1 mv = 8.5 m/s

A 1.4 kg ball on a string 1.1 m long is swung in a vertical circle. At the lowest point it moves at 8.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 1.1 mv = 8.5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 14333 N
  2. 2. ac = 0.7692 m/s²
  3. 3. vmax = 14.01 m/s
  4. 4. v = 17.69 m/s
  5. 5. Ttop = 49.96 N
  6. 6. T = 105.7 N

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