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 = 70 m28 m/sac​ = ?

A 1700 kg car drives around a flat curve of radius 70 m at a constant 28 m/s. Find its centripetal acceleration ac.

m = 1700 kgv = 28 m/sr = 70 m
ac = m/s²
2.Easy
r = 0.6 mvmax​ = ?

A 0.7 kg stone is whirled in a horizontal circle of radius 0.6 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 = 0.7 kgr = 0.6 mTmax = 60 N
vmax = m/s
3.Medium
r = 45 m8 m/s

A 1400 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 45 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1400 kgv = 8 m/sr = 45 mg = 9.81 m/s²
N = N
4.Medium
r = 140 mvmax​ = ?

A car takes a flat curve of radius 140 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 = 140 mμs = 0.5g = 9.81 m/s²
vmax = m/s
5.Hard
r = 0.7 mv = 4 m/s

A 1.4 kg ball on a string 0.7 m long is swung in a vertical circle. At the lowest point it moves at 4 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1.4 kgr = 0.7 mv = 4 m/sg = 9.81 m/s²
T = N
6.Hard
r = 1 m8 m/svtop​ = ?

A 1.2 kg ball on a light string 1 m long is swung in a vertical circle. At the lowest point its speed is 8 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.2 kgr = 1 mvbottom = 8 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. ac = 11.2 m/s²
  2. 2. vmax = 7.171 m/s
  3. 3. N = 11743 N
  4. 4. vmax = 26.2 m/s
  5. 5. T = 45.73 N
  6. 6. Ttop = 17.94 N

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