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 = 2 mvmax​ = ?

A 1.9 kg stone is whirled in a horizontal circle of radius 2 m on a smooth, level table, held by a string that breaks at a tension of 40 N. Find the highest speed vmax the stone can have.

m = 1.9 kgr = 2 mTmax = 40 N
vmax = m/s
2.Easy
r = 120 m24 m/sF = ?

A 600 kg car drives around a flat curve of radius 120 m at a constant 24 m/s. Find the inward (centripetal) force Fc needed.

m = 600 kgv = 24 m/sr = 120 m
Fc = N
3.Medium
r = 125 mvmax​ = ?

A car takes a flat curve of radius 125 m. The coefficient of static friction between tyres and road is 0.7. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 125 mμs = 0.7g = 9.81 m/s²
vmax = m/s
4.Medium
r = 45 m7 m/s

A 1700 kg car drives over the top of a hump in the road at 7 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 = 1700 kgv = 7 m/sr = 45 mg = 9.81 m/s²
N = N
5.Hard
R = 5.5 mh = 26.95 m

A 1.5 kg cart is released from rest at a height of 26.95 m on a frictionless track and runs through a vertical loop of radius 5.5 m. Use g = 9.81 m/s². Find the normal force Ntop of the track on the cart at the top of the loop.

m = 1.5 kgh = 26.95 mR = 5.5 mg = 9.81 m/s²
Ntop = N
6.Hard
r = 0.9 m11 m/svtop​ = ?

A 1.8 kg ball on a light string 0.9 m long is swung in a vertical circle. At the lowest point its speed is 11 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 = 0.9 mvbottom = 11 m/sg = 9.81 m/s²
Ttop = N

Answer key

  1. 1. vmax = 6.489 m/s
  2. 2. Fc = 2880 N
  3. 3. vmax = 29.3 m/s
  4. 4. N = 14826 N
  5. 5. Ntop = 70.63 N
  6. 6. Ttop = 153.7 N

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