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 = 50 m18 m/sac​ = ?

A 1400 kg car drives around a flat curve of radius 50 m at a constant 18 m/s. Find its centripetal acceleration ac.

m = 1400 kgv = 18 m/sr = 50 m
ac = m/s²
2.Easy
r = ?160 km/h

For passenger comfort the centripetal acceleration on a railway curve must not exceed 0.5 m/s². What is the smallest radius rmin for a curve taken at 160 km/h?

v = 160 km/hamax = 0.5 m/s²
rmin = m
3.Medium
r = 90 m9 m/s

A 1500 kg car drives over the top of a hump in the road at 9 m/s. The top of the hump is a circular arc of radius 90 m. Use g = 9.81 m/s². Find the normal force N of the road on the car at the top.

m = 1500 kgv = 9 m/sr = 90 mg = 9.81 m/s²
N = N
4.Medium
r = 3.7 mω = ?

In a fairground rotor, riders stand against the wall of a vertical cylinder of radius 3.7 m. When it spins fast enough the floor drops away and friction holds them up. The coefficient of static friction is 0.7. Use g = 9.81 m/s². Find the smallest angular speed ω in rad/s.

r = 3.7 mμs = 0.7g = 9.81 m/s²
ω = rad/s
5.Hard
r = 0.6 m9.5 m/svtop​ = ?

A 1.9 kg ball on a light string 0.6 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 = 1.9 kgr = 0.6 mvbottom = 9.5 m/sg = 9.81 m/s²
Ttop = N
6.Hard
r = 1.4 mv = 6 m/s

A 1 kg ball on a string 1.4 m long is swung in a vertical circle. At the lowest point it moves at 6 m/s. Use g = 9.81 m/s². Find the tension T in the string at the lowest point.

m = 1 kgr = 1.4 mv = 6 m/sg = 9.81 m/s²
T = N

Answer key

  1. 1. ac = 6.48 m/s²
  2. 2. rmin = 3951 m
  3. 3. N = 13365 N
  4. 4. ω = 1.946 rad/s
  5. 5. Ttop = 192.6 N
  6. 6. T = 35.52 N

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