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 = 1 mGOd = 0.4 mm = 10.5 kg

A uniform slender rod of mass 10.5 kg and length 1 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10.5 kgL = 1 md = 0.4 m
IO = kg·m²
2.Easy
L = 2.4 mGOd = 0.6 mm = 4 kg

A uniform slender rod of mass 4 kg and length 2.4 m rotates about an axis O perpendicular to the rod, 0.6 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4 kgL = 2.4 md = 0.6 m
IO = kg·m²
3.Medium
L = 2.5 mm = 14 kgα

A uniform slender rod of mass 14 kg and length 2.5 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 = 14 kgL = 2.5 mg = 9.81 m/s²
atip = m/s²
4.Medium
14 kgaαM = 14.5 kgR = 0.35 m

A 14 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 14.5 kg and radius 0.35 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 = 14 kgM = 14.5 kgR = 0.35 mg = 9.81 m/s²
a = m/s²
5.Hard
θ = 15°vs = 7 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 15° to the horizontal. Use g = 9.81 m/s². Its radius is 0.15 m. Find its angular velocity ω after it has rolled 7 m along the slope.

θ = 15°s = 7 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.15 m
ω = rad/s
6.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 acceleration a of its centre.

θ = 40°I = m·r²g = 9.81 m/s²
a = m/s²

Answer key

  1. 1. IO = 2.555 kg·m²
  2. 2. IO = 3.36 kg·m²
  3. 3. atip = 14.71 m/s²
  4. 4. a = 6.463 m/s²
  5. 5. ω = 33.59 rad/s
  6. 6. a = 3.153 m/s²

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