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 = 0.7 mGOd = 0.3 mm = 3 kg

A uniform slender rod of mass 3 kg and length 0.7 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 0.7 md = 0.3 m
IO = kg·m²
2.Easy
k = 0.5 m0 → 1400 rpm160 kg

A flywheel of mass 160 kg with a radius of gyration of 0.5 m is accelerated uniformly from rest to 1400 rpm. This takes 26 s. Ignoring friction, find the constant torque T needed.

m = 160 kgk = 0.5 mn1 = 0 rpmn2 = 1400 rpmt = 26 s
T = N·m
3.Medium
n = 1500 rpmTb​ = 110 N·mI = 10 kg·m²

A flywheel with a moment of inertia of 10 kg·m² spins at 1500 rpm. A brake applies a constant friction torque of 110 N·m. How long t does it take to stop?

I = 10 kg·m²n = 1500 rpmTb = 110 N·m
t = s
4.Medium
ω = ?L = 1.9 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 1.9 m is pinned at one end and released from rest in a horizontal position. 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 = 7.5 kgL = 1.9 mg = 9.81 m/s²
ω = rad/s
5.Hard
θ = 30°as = 7.5 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 7.5 m down the slope?

θ = 30°I = (2/5)·m·r²g = 9.81 m/s²s = 7.5 m
t = s
6.Hard
θ = 25°as = 1.5 m

A hollow 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 1.5 m down the slope?

θ = 25°I = (2/3)·m·r²g = 9.81 m/s²s = 1.5 m
t = s

Answer key

  1. 1. IO = 0.3925 kg·m²
  2. 2. T = 225.6 N·m
  3. 3. t = 14.28 s
  4. 4. ω = 3.936 rad/s
  5. 5. t = 2.069 s
  6. 6. t = 1.098 s

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