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 m17 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 150 m at a constant 17 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 17 m/sr = 150 m
ac = m/s²
2.Easy
r = 1.4 mvmax​ = ?

A 0.2 kg stone is whirled in a horizontal circle of radius 1.4 m on a smooth, level table, held by a string that breaks at a tension of 60 N. Find the highest speed vmax the stone can have.

m = 0.2 kgr = 1.4 mTmax = 60 N
vmax = m/s
3.Medium
r = 85 mvmax​ = ?

A car takes a flat curve of radius 85 m. The coefficient of static friction between tyres and road is 0.8. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 85 mμs = 0.8g = 9.81 m/s²
vmax = m/s
4.Medium
r = 2.2 mn = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 2.2 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 = 2.2 mμs = 0.5g = 9.81 m/s²
n = rpm
5.Hard
r = 1.2 m10.5 m/svtop​ = ?

A 1.1 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 10.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.1 kgr = 1.2 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1 mv = ?

A ball on a string 1 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 = 1 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. ac = 1.927 m/s²
  2. 2. vmax = 20.49 m/s
  3. 3. vmax = 25.83 m/s
  4. 4. n = 28.52 rpm
  5. 5. Ttop = 47.11 N
  6. 6. vmin = 3.132 m/s

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