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 = 0.5 mGOd = 0.25 mm = 3 kg

A uniform slender rod of mass 3 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.25 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 3 kgL = 0.5 md = 0.25 m
IO = kg·m²
2.Easy
k = 0.6 m500 → 1800 rpm130 kg

A flywheel of mass 130 kg with a radius of gyration of 0.6 m is accelerated uniformly from 500 rpm to 1800 rpm. This takes 15 s. Ignoring friction, find the constant torque T needed.

m = 130 kgk = 0.6 mn1 = 500 rpmn2 = 1800 rpmt = 15 s
T = N·m
3.Medium
L = 1.5 mm = 3.5 kgα

A uniform slender rod of mass 3.5 kg and length 1.5 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 = 3.5 kgL = 1.5 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 2100 rpmTb​ = 165 N·mI = 33.5 kg·m²

A flywheel with a moment of inertia of 33.5 kg·m² spins at 2100 rpm. A brake applies a constant friction torque of 165 N·m. How many revolutions N does the flywheel make before it stops?

I = 33.5 kg·m²n = 2100 rpmTb = 165 N·m
N = rev
5.Hard
θ = 25°vs = 2 m

A solid cylinder starts from rest and rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Its radius is 0.35 m. Find its angular velocity ω after it has rolled 2 m along the slope.

θ = 25°s = 2 mI = ½·m·r²g = 9.81 m/s²r = 0.35 m
ω = rad/s
6.Hard
θ = 40°vs = 7.5 m

A thin hoop starts from rest and rolls without slipping down a slope inclined at 40° to the horizontal. Use g = 9.81 m/s². Its radius is 0.4 m. Find its angular velocity ω after it has rolled 7.5 m along the slope.

θ = 40°s = 7.5 mI = m·r²g = 9.81 m/s²r = 0.4 m
ω = rad/s

Answer key

  1. 1. IO = 0.25 kg·m²
  2. 2. T = 424.7 N·m
  3. 3. α = 9.81 rad/s²
  4. 4. N = 781.4 rev
  5. 5. ω = 9.5 rad/s
  6. 6. ω = 17.19 rad/s

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