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 = 1.8 mvmax​ = ?

A 1.4 kg stone is whirled in a horizontal circle of radius 1.8 m on a smooth, level table, held by a string that breaks at a tension of 190 N. Find the highest speed vmax the stone can have.

m = 1.4 kgr = 1.8 mTmax = 190 N
vmax = m/s
2.Easy
r = 140 m24 m/sac​ = ?

A 600 kg car drives around a flat curve of radius 140 m at a constant 24 m/s. Find its centripetal acceleration ac.

m = 600 kgv = 24 m/sr = 140 m
ac = m/s²
3.Medium
r = 95 mvmax​ = ?

A car takes a flat curve of radius 95 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 = 95 mμs = 0.5g = 9.81 m/s²
vmax = m/s
4.Medium
r = 25 m8 m/s

A 1800 kg car drives over the top of a hump in the road at 8 m/s. The top of the hump is a circular arc of radius 25 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1800 kgv = 8 m/sr = 25 mg = 9.81 m/s²
N = N
5.Hard
r = 1.2 m10 m/svtop​ = ?

A 1.8 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 10 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 = 1.2 mvbottom = 10 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. vmax = 15.63 m/s
  2. 2. ac = 4.114 m/s²
  3. 3. vmax = 21.59 m/s
  4. 4. N = 13050 N
  5. 5. Ttop = 61.71 N
  6. 6. vmin = 3.132 m/s

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