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 = 1.2 mGOd = 0.6 mm = 1 kg

A uniform slender rod of mass 1 kg and length 1.2 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 = 1 kgL = 1.2 md = 0.6 m
IO = kg·m²
2.Easy
Or = 0.15 mL = 0.4 m0.55 m0.5 kg10 kg

A pendulum is made of a uniform slender rod (0.5 kg, 0.4 m long) pivoted at its top end O, with a thin solid disc of mass 10 kg and radius 0.15 m fixed to its lower end. The disc swings in its own plane and its centre is 0.55 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 0.5 kgL = 0.4 mmdisc = 10 kgr = 0.15 md = 0.55 m
IO = kg·m²
3.Medium
n = 2600 rpmTb​ = 75 N·mI = 16 kg·m²

A flywheel with a moment of inertia of 16 kg·m² spins at 2600 rpm. A brake applies a constant friction torque of 75 N·m. How long t does it take to stop?

I = 16 kg·m²n = 2600 rpmTb = 75 N·m
t = s
4.Medium
L = 2.7 mm = 20 kgα

A uniform slender rod of mass 20 kg and length 2.7 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 = 20 kgL = 2.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
4.5 m/sω

A solid cylinder of mass 17.5 kg rolls without slipping at 4.5 m/s. Find its rotational kinetic energy Erot.

m = 17.5 kgv = 4.5 m/sI = ½·m·r²
Erot = J
6.Hard
θ = 40°as = 8.5 m

A solid sphere rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 8.5 m down the slope?

θ = 40°I = (2/5)·m·r²g = 9.81 m/s²s = 8.5 m
t = s

Answer key

  1. 1. IO = 0.48 kg·m²
  2. 2. IO = 3.164 kg·m²
  3. 3. t = 58.08 s
  4. 4. atip = 14.71 m/s²
  5. 5. Erot = 88.59 J
  6. 6. t = 1.943 s

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