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
L = 2 mGOd = 0.8 mm = 11 kg

A uniform slender rod of mass 11 kg and length 2 m rotates about an axis O perpendicular to the rod, 0.8 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11 kgL = 2 md = 0.8 m
IO = kg·m²
2.Easy
Or = 0.2 mL = 0.5 m0.7 m3.5 kg5 kg

A pendulum is made of a uniform slender rod (3.5 kg, 0.5 m long) pivoted at its top end O, with a thin solid disc of mass 5 kg and radius 0.2 m fixed to its lower end. The disc swings in its own plane and its centre is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3.5 kgL = 0.5 mmdisc = 5 kgr = 0.2 md = 0.7 m
IO = kg·m²
3.Medium
10.5 kgaαM = 4.5 kgR = 0.2 m

A 10.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 4.5 kg and radius 0.2 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 10.5 kgM = 4.5 kgR = 0.2 mg = 9.81 m/s²
a = m/s²
4.Medium
L = 0.9 mm = 4.5 kgα

A uniform slender rod of mass 4.5 kg and length 0.9 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 4.5 kgL = 0.9 mg = 9.81 m/s²
atip = m/s²
5.Hard
θ = 40°a

A thin hoop rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 40°I = m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 30°a

A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 30°I = (2/5)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 10.71 kg·m²
  2. 2. IO = 2.842 kg·m²
  3. 3. a = 8.079 m/s²
  4. 4. atip = 14.71 m/s²
  5. 5. μs = 0.4195
  6. 6. a = 3.504 m/s²

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