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 = 2.7 mGOd = 1.05 mm = 6 kg

A uniform slender rod of mass 6 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 1.05 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 6 kgL = 2.7 md = 1.05 m
IO = kg·m²
2.Easy
Or = 0.25 mL = 0.5 m0.75 m2.5 kg1.5 kg

A pendulum is made of a uniform slender rod (2.5 kg, 0.5 m long) pivoted at its top end O, with a solid sphere of mass 1.5 kg and radius 0.25 m fixed to its lower end. The centre of the sphere is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 0.5 mmsphere = 1.5 kgr = 0.25 md = 0.75 m
IO = kg·m²
3.Medium
L = 3 mm = 14 kgα

A uniform slender rod of mass 14 kg and length 3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 14 kgL = 3 mg = 9.81 m/s²
α = rad/s²
4.Medium
v = ?1.5 kgL = 2.4 mm = 9 kg

A uniform slender rod of mass 9 kg and length 2.4 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 speed v of the free end as the rod swings through the vertical position.

m = 9 kgL = 2.4 mmball = 1.5 kgg = 9.81 m/s²
v = m/s
5.Hard
9.5 m/sω

A solid cylinder of mass 3.5 kg rolls without slipping at 9.5 m/s. Find its rotational kinetic energy Erot.

m = 3.5 kgv = 9.5 m/sI = ½·m·r²
Erot = J
6.Hard
θ = 15°a

A solid sphere rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 15°I = (2/5)·m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 10.26 kg·m²
  2. 2. IO = 1.09 kg·m²
  3. 3. α = 4.905 rad/s²
  4. 4. v = 7.924 m/s
  5. 5. Erot = 78.97 J
  6. 6. a = 1.814 m/s²

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