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 = 150 m27 m/sac​ = ?

A 1300 kg car drives around a flat curve of radius 150 m at a constant 27 m/s. Find its centripetal acceleration ac.

m = 1300 kgv = 27 m/sr = 150 m
ac = m/s²
2.Easy
r = ?250 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 2 m/s². What is the smallest radius rmin for a curve taken at 250 km/h?

v = 250 km/hamax = 2 m/s²
rmin = m
3.Medium
r = 60 m13 m/s

A 1800 kg car drives over the top of a hump in the road at 13 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 = 1800 kgv = 13 m/sr = 60 mg = 9.81 m/s²
N = N
4.Medium
r = 80 m5 m/s

A 900 kg car drives over the top of a hump in the road at 5 m/s. The top of the hump is a circular arc of radius 80 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 900 kgv = 5 m/sr = 80 mg = 9.81 m/s²
N = N
5.Hard
r = 1.2 m11.5 m/svtop​ = ?

A 0.6 kg ball on a light string 1.2 m long is swung in a vertical circle. At the lowest point its speed is 11.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 0.6 kgr = 1.2 mvbottom = 11.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
R = 3 mh = 13.2 m

A 0.5 kg cart is released from rest at a height of 13.2 m on a frictionless track and runs through a vertical loop of radius 3 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 = 0.5 kgh = 13.2 mR = 3 mg = 9.81 m/s²
Ntop = N

Answer key

  1. 1. ac = 4.86 m/s²
  2. 2. rmin = 2411 m
  3. 3. N = 12588 N
  4. 4. N = 8548 N
  5. 5. Ttop = 36.7 N
  6. 6. Ntop = 18.64 N

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