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 = 90 m27 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 90 m at a constant 27 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 27 m/sr = 90 m
ac = m/s²
2.Easy
r = ?120 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 120 km/h?

v = 120 km/hamax = 0.5 m/s²
rmin = m
3.Medium
r = 35 m6 m/s

A 1200 kg car drives over the top of a hump in the road at 6 m/s. The top of the hump is a circular arc of radius 35 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1200 kgv = 6 m/sr = 35 mg = 9.81 m/s²
N = N
4.Medium
r = 4 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 4 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.5. Use g = 9.81 m/s². Find the smallest rotation rate n in revolutions per minute.

r = 4 mμs = 0.5g = 9.81 m/s²
n = rpm
5.Hard
r = 0.6 mv = 6.5 m/s

A 0.7 kg ball on a string 0.6 m long is swung in a vertical circle. At the lowest point it moves at 6.5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 0.7 kgr = 0.6 mv = 6.5 m/sg = 9.81 m/s²
T = N
6.Hard
r = 0.8 mv = 5 m/s

A 1.5 kg ball on a string 0.8 m long is swung in a vertical circle. At the lowest point it moves at 5 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.5 kgr = 0.8 mv = 5 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. ac = 8.1 m/s²
  2. 2. rmin = 2222 m
  3. 3. N = 10538 N
  4. 4. n = 21.15 rpm
  5. 5. T = 56.16 N
  6. 6. T = 61.59 N

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