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 = 1.8 mGOd = 0.65 mm = 1.5 kg

A uniform slender rod of mass 1.5 kg and length 1.8 m rotates about an axis O perpendicular to the rod, 0.65 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1.5 kgL = 1.8 md = 0.65 m
IO = kg·m²
2.Easy
Or = 0.05 mL = 1.3 m1.35 m2.5 kg6 kg

A pendulum is made of a uniform slender rod (2.5 kg, 1.3 m long) pivoted at its top end O, with a solid sphere of mass 6 kg and radius 0.05 m fixed to its lower end. The centre of the sphere is 1.35 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 2.5 kgL = 1.3 mmsphere = 6 kgr = 0.05 md = 1.35 m
IO = kg·m²
3.Medium
8 kgaαM = 3.5 kgR = 0.45 m

An 8 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 3.5 kg and radius 0.45 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the angular acceleration α of the pulley.

m = 8 kgM = 3.5 kgR = 0.45 mg = 9.81 m/s²
α = rad/s²
4.Medium
n = 1100 rpmP = 27.5 kW

A shaft transmits 27.5 kW at 1100 rpm. Find the torque T in the shaft.

P = 27.5 kWn = 1100 rpm
T = N·m
5.Hard
1 m/sω

A hollow sphere of mass 12 kg rolls without slipping at 1 m/s. What percentage p of its total kinetic energy is rotational?

m = 12 kgv = 1 m/sI = (2/3)·m·r²
p = %
6.Hard
0.7 m0.25 mn1​ = 20 rpm

A person stands on a frictionless turntable and holds a 5 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 4.5 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 4.5 kg·m²m = 2 × 5 kgr1 = 0.7 mr2 = 0.25 mn1 = 20 rpm
n2 = rpm

Answer key

  1. 1. IO = 1.039 kg·m²
  2. 2. IO = 12.35 kg·m²
  3. 3. α = 17.89 rad/s²
  4. 4. T = 238.7 N·m
  5. 5. p = 40 %
  6. 6. n2 = 36.68 rpm

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