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 = 0.8 mvmax​ = ?

A 0.5 kg stone is whirled in a horizontal circle of radius 0.8 m on a smooth, level table, held by a string that breaks at a tension of 130 N. Find the highest speed vmax the stone can have.

m = 0.5 kgr = 0.8 mTmax = 130 N
vmax = m/s
2.Easy
r = 110 m23 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 110 m at a constant 23 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 23 m/sr = 110 m
ac = m/s²
3.Medium
r = 105 mvmax​ = ?

A car takes a flat curve of radius 105 m. The coefficient of static friction between tyres and road is 0.5. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 105 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 60 m10 m/s

A 1400 kg car drives over the top of a hump in the road at 10 m/s. The top of the hump is a circular arc of radius 60 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1400 kgv = 10 m/sr = 60 mg = 9.81 m/s²
N = N
5.Hard
r = 1.3 m10.5 m/svtop​ = ?

A 1.8 kg ball on a light string 1.3 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 = 1.8 kgr = 1.3 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1.3 mv = ?

A ball on a string 1.3 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 = 1.3 mg = 9.81 m/s²
vmin = m/s

Answer key

  1. 1. vmax = 14.42 m/s
  2. 2. ac = 4.809 m/s²
  3. 3. vmax = 22.69 m/s
  4. 4. N = 11401 N
  5. 5. Ttop = 64.36 N
  6. 6. vmin = 3.571 m/s

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