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 = 20 m10 m/sF = ?

A 1400 kg car drives around a flat curve of radius 20 m at a constant 10 m/s. Find the inward (centripetal) force Fc needed.

m = 1400 kgv = 10 m/sr = 20 m
Fc = N
2.Easy
r = 0.3 mvmax​ = ?

A 0.9 kg stone is whirled in a horizontal circle of radius 0.3 m on a smooth, level table, held by a string that breaks at a tension of 20 N. Find the highest speed vmax the stone can have.

m = 0.9 kgr = 0.3 mTmax = 20 N
vmax = m/s
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 0.6. Use g = 9.81 m/s². Find the highest speed vmax at which the car can take the curve without skidding.

r = 95 mμs = 0.6g = 9.81 m/s²
vmax = m/s
4.Medium
r = 85 m14 m/s

A 1000 kg car drives over the top of a hump in the road at 14 m/s. The top of the hump is a circular arc of radius 85 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1000 kgv = 14 m/sr = 85 mg = 9.81 m/s²
N = N
5.Hard
r = 0.7 m10.5 m/svtop​ = ?

A 0.8 kg ball on a light string 0.7 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 = 0.8 kgr = 0.7 mvbottom = 10.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
R = 10 mh = 37 m

A 1.5 kg cart is released from rest at a height of 37 m on a frictionless track and runs through a vertical loop of radius 10 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 = 37 mR = 10 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. Fc = 7000 N
  2. 2. vmax = 2.582 m/s
  3. 3. vmax = 23.65 m/s
  4. 4. N = 7504 N
  5. 5. Ttop = 86.76 N
  6. 6. Ntop = 35.32 N

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