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 = 2.1 mGOd = 1 mm = 10 kg

A uniform slender rod of mass 10 kg and length 2.1 m rotates about an axis O perpendicular to the rod, 1 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 10 kgL = 2.1 md = 1 m
IO = kg·m²
2.Easy
k = 0.55 m700 → 1100 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.55 m is accelerated uniformly from 700 rpm to 1100 rpm. This takes 8 s. Ignoring friction, find the constant torque T needed.

m = 150 kgk = 0.55 mn1 = 700 rpmn2 = 1100 rpmt = 8 s
T = N·m
3.Medium
L = 1 mm = 13 kgα

A uniform slender rod of mass 13 kg and length 1 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 = 13 kgL = 1 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 1000 rpmP = 199.5 kW

A shaft transmits 199.5 kW at 1000 rpm. Find the torque T in the shaft.

P = 199.5 kWn = 1000 rpm
T = N·m
5.Hard
θ = 10°vs = 6.5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Its radius is 0.2 m. Find its angular velocity ω after it has rolled 6.5 m along the slope.

θ = 10°s = 6.5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.2 m
ω = rad/s
6.Hard
θ = 35°vs = 5 m

A solid sphere starts from rest and rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². Its radius is 0.3 m. Find its angular velocity ω after it has rolled 5 m along the slope.

θ = 35°s = 5 mI = (2/5)·m·r²g = 9.81 m/s²r = 0.3 m
ω = rad/s

Answer key

  1. 1. IO = 13.68 kg·m²
  2. 2. T = 237.6 N·m
  3. 3. α = 14.71 rad/s²
  4. 4. T = 1905 N·m
  5. 5. ω = 19.89 rad/s
  6. 6. ω = 21.13 rad/s

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