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
R = 0.2 mn = 2800 rpm230 kg

A flywheel is a uniform solid disc of mass 230 kg and radius 0.2 m. It spins at 2800 rpm. Find its kinetic energy Ek in kJ.

M = 230 kgR = 0.2 mn = 2800 rpm
Ek = kJ
2.Easy
L = 2.9 mGOd = 0.7 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 2.9 m rotates about an axis O perpendicular to the rod, 0.7 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4.5 kgL = 2.9 md = 0.7 m
IO = kg·m²
3.Medium
n = 1400 rpmP = 129 kW

A shaft transmits 129 kW at 1400 rpm. Find the torque T in the shaft.

P = 129 kWn = 1400 rpm
T = N·m
4.Medium
L = 0.6 mm = 2.5 kgα

A uniform slender rod of mass 2.5 kg and length 0.6 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 2.5 kgL = 0.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
4.5 m/sω

A solid sphere of mass 18.5 kg rolls without slipping at 4.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 18.5 kgv = 4.5 m/sI = (2/5)·m·r²
p = %
6.Hard
6.5 m/sω

A solid cylinder of mass 6 kg rolls without slipping at 6.5 m/s. Find its rotational kinetic energy Erot.

m = 6 kgv = 6.5 m/sI = ½·m·r²
Erot = J

Answer key

  1. 1. Ek = 197.7 kJ
  2. 2. IO = 5.359 kg·m²
  3. 3. T = 879.9 N·m
  4. 4. atip = 14.71 m/s²
  5. 5. p = 28.57 %
  6. 6. Erot = 63.38 J

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