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 = 0.45 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 3 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4.5 kgL = 3 md = 0.45 m
IO = kg·m²
2.Easy
Or = 0.05 mL = 1.2 m1.25 m2.5 kg4.5 kg

A pendulum is made of a uniform slender rod (2.5 kg, 1.2 m long) pivoted at its top end O, with a solid sphere of mass 4.5 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.25 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 1.2 mmsphere = 4.5 kgr = 0.05 md = 1.25 m
IO = kg·m²
3.Medium
n = 2100 rpmTb​ = 175 N·mI = 22 kg·m²

A flywheel with a moment of inertia of 22 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 175 N·m. How many revolutions N does the flywheel make before it stops?

I = 22 kg·m²n = 2100 rpmTb = 175 N·m
N = rev
4.Medium
n = 2700 rpmTb​ = 50 N·mI = 36 kg·m²

A flywheel with a moment of inertia of 36 kg·m² spins at 2700 rpm. A brake applies a constant friction torque of 50 N·m. How long t does it take to stop?

I = 36 kg·m²n = 2700 rpmTb = 50 N·m
t = s
5.Hard
θ = 20°a

A thin hoop rolls without slipping down a slope inclined at 20° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 20°I = m·r²g = 9.81 m/s²
μs =
6.Hard
θ = 35°as = 9.5 m

A solid cylinder rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 9.5 m down the slope?

θ = 35°I = ½·m·r²g = 9.81 m/s²s = 9.5 m
t = s

Answer key

  1. 1. IO = 4.286 kg·m²
  2. 2. IO = 8.236 kg·m²
  3. 3. N = 483.8 rev
  4. 4. t = 203.6 s
  5. 5. μs = 0.182
  6. 6. t = 2.251 s

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