Rigid-body rotation worksheet with answers

Free printable Rigid-body rotation 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
k = 0.5 mn = 300 rpm40 kg

A flywheel of mass 40 kg has a radius of gyration of 0.5 m about its axis. It spins at 300 rpm. Find its kinetic energy Ek in kJ.

M = 40 kgk = 0.5 mn = 300 rpm
Ek = kJ
2.Easy
R = 0.8 mn = 1700 rpm290 kg

A flywheel is a uniform solid disc of mass 290 kg and radius 0.8 m. It spins at 1700 rpm. Find its kinetic energy Ek in kJ.

M = 290 kgR = 0.8 mn = 1700 rpm
Ek = kJ
3.Medium
L = 0.8 mm = 5.5 kgα

A uniform slender rod of mass 5.5 kg and length 0.8 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the vertical force R that the pin exerts on the rod just after release.

m = 5.5 kgL = 0.8 mg = 9.81 m/s²
R = N
4.Medium
ω = ?1.5 kgL = 0.7 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.7 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 9 kgL = 0.7 mmball = 1.5 kgg = 9.81 m/s²
ω = rad/s
5.Hard
3 m/sω

A hollow sphere of mass 11 kg rolls without slipping at 3 m/s. Find its rotational kinetic energy Erot.

m = 11 kgv = 3 m/sI = (2/3)·m·r²
Erot = J
6.Hard
θ = 30°a

A thin hoop rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 30°I = m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. Ek = 4.935 kJ
  2. 2. Ek = 1471 kJ
  3. 3. R = 13.49 N
  4. 4. ω = 6.113 rad/s
  5. 5. Erot = 33 J
  6. 6. μs = 0.2887

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