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 = 150 m28 m/sF = ?

A 1700 kg car drives around a flat curve of radius 150 m at a constant 28 m/s. Find the inward (centripetal) force Fc needed.

m = 1700 kgv = 28 m/sr = 150 m
Fc = N
2.Easy
r = 1.2 mv = ?30 rpm

A small object sits 120 cm from the axis of a disc that turns at a steady 30 revolutions per minute. Find the speed v of the object.

n = 30 rpmr = 1.2 m
v = m/s
3.Medium
r = 115 m7 m/s

An 800 kg car drives over the top of a hump in the road at 7 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 = 800 kgv = 7 m/sr = 115 mg = 9.81 m/s²
N = N
4.Medium
L = 1.4 m45°

A small ball on a string of length 1.4 m moves in a horizontal circle so that the string makes a constant angle of 45° with the vertical (a conical pendulum). Use g = 9.81 m/s². Find the speed v of the ball.

L = 1.4 mθ = 45°g = 9.81 m/s²
v = m/s
5.Hard
r = 0.8 mv = ?

A ball on a string 0.8 m long is swung in a vertical circle. Use g = 9.81 m/s². What is the smallest speed vmin at the top for which the string just stays tight?

r = 0.8 mg = 9.81 m/s²
vmin = m/s
6.Hard
r = 0.9 mv = 6 m/s

A 1.2 kg ball on a string 0.9 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 = 1.2 kgr = 0.9 mv = 6 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. Fc = 8885 N
  2. 2. v = 3.77 m/s
  3. 3. N = 7507 N
  4. 4. v = 3.116 m/s
  5. 5. vmin = 2.801 m/s
  6. 6. T = 59.77 N

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