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 = 0.4 mm = 3.5 kg

A uniform slender rod of mass 3.5 kg and length 2 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 = 3.5 kgL = 2 md = 0.4 m
IO = kg·m²
2.Easy
k = 0.2 mn = 1200 rpm150 kg

A flywheel of mass 150 kg has a radius of gyration of 0.2 m about its axis. It spins at 1200 rpm. Find its kinetic energy Ek in kJ.

M = 150 kgk = 0.2 mn = 1200 rpm
Ek = kJ
3.Medium
4.5 kgaαM = 8 kgR = 0.2 m

A 4.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 8 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 angular acceleration α of the pulley.

m = 4.5 kgM = 8 kgR = 0.2 mg = 9.81 m/s²
α = rad/s²
4.Medium
L = 2.3 mm = 2 kgα

A uniform slender rod of mass 2 kg and length 2.3 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 = 2 kgL = 2.3 mg = 9.81 m/s²
α = rad/s²
5.Hard
400 m/s10 g0.64 mL = 1.6 m7 kg

A uniform slender rod of mass 7 kg and length 1.6 m hangs at rest from a frictionless pivot at its top end. A 10 g bullet moving horizontally at 400 m/s hits the rod 0.64 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 7 kgL = 1.6 mm = 10 gv = 400 m/sd = 0.64 m
ω = rad/s
6.Hard
θ = 30°as = 6.5 m

A solid sphere rolls without slipping down a slope inclined at 30° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 6.5 m down the slope?

θ = 30°I = (2/5)·m·r²g = 9.81 m/s²s = 6.5 m
t = s

Answer key

  1. 1. IO = 1.727 kg·m²
  2. 2. Ek = 47.37 kJ
  3. 3. α = 25.97 rad/s²
  4. 4. α = 6.398 rad/s²
  5. 5. ω = 0.4283 rad/s
  6. 6. t = 1.926 s

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