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 = 3 mGOd = 1.1 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 3 m rotates about an axis O perpendicular to the rod, 1.1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5.5 kgL = 3 md = 1.1 m
IO = kg·m²
2.Easy
k = 0.2 m500 → 900 rpm120 kg

A flywheel of mass 120 kg with a radius of gyration of 0.2 m is accelerated uniformly from 500 rpm to 900 rpm. This takes 12 s. Ignoring friction, find the constant torque T needed.

m = 120 kgk = 0.2 mn1 = 500 rpmn2 = 900 rpmt = 12 s
T = N·m
3.Medium
ω = ?3 kgL = 1.6 mm = 2 kg

A uniform slender rod of mass 2 kg and length 1.6 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 3 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 2 kgL = 1.6 mmball = 3 kgg = 9.81 m/s²
ω = rad/s
4.Medium
0 → 2400 rpmI = 7.5 kg·m²

A motor brings a flywheel with a moment of inertia of 7.5 kg·m² from rest up to 2400 rpm in 31 s. Ignoring losses, find the average power Pavg it delivers, in kW.

I = 7.5 kg·m²n = 2400 rpmt = 31 s
Pavg = kW
5.Hard
θ = 10°a

A solid cylinder rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the acceleration a of its centre.

θ = 10°I = ½·m·r²g = 9.81 m/s²
a = m/s²
6.Hard
θ = 25°as = 8 m

A solid sphere rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 8 m down the slope?

θ = 25°I = (2/5)·m·r²g = 9.81 m/s²s = 8 m
t = s

Answer key

  1. 1. IO = 10.78 kg·m²
  2. 2. T = 16.76 N·m
  3. 3. ω = 3.657 rad/s
  4. 4. Pavg = 7.641 kW
  5. 5. a = 1.136 m/s²
  6. 6. t = 2.324 s

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