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 = ?240 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 1 m/s². What is the smallest radius rmin for a curve taken at 240 km/h?

v = 240 km/hamax = 1 m/s²
rmin = m
2.Easy
r = 130 m11 m/sac​ = ?

A 1300 kg car drives around a flat curve of radius 130 m at a constant 11 m/s. Find its centripetal acceleration ac.

m = 1300 kgv = 11 m/sr = 130 m
ac = m/s²
3.Medium
r = 60 m12 m/s

A 1200 kg car drives over the top of a hump in the road at 12 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 = 1200 kgv = 12 m/sr = 60 mg = 9.81 m/s²
N = N
4.Medium
r = 75 m14 m/s

An 800 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 75 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 800 kgv = 14 m/sr = 75 mg = 9.81 m/s²
N = N
5.Hard
r = 0.5 m9.5 m/svtop​ = ?

A 1.3 kg ball on a light string 0.5 m long is swung in a vertical circle. At the lowest point its speed is 9.5 m/s. Ignore air resistance and use g = 9.81 m/s². Find the tension Ttop in the string at the highest point.

m = 1.3 kgr = 0.5 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
R = 7.5 mh = ?

A small cart is released from rest on a frictionless track and runs into a vertical loop of radius 7.5 m. From what minimum height hmin above the bottom of the loop must it start to stay on the track at the top of the loop?

R = 7.5 mv₀ = 0
hmin = m

Answer key

  1. 1. rmin = 4444 m
  2. 2. ac = 0.9308 m/s²
  3. 3. N = 8892 N
  4. 4. N = 5757 N
  5. 5. Ttop = 170.9 N
  6. 6. hmin = 18.75 m

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