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 mGOd = 0.15 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 1 m rotates about an axis O perpendicular to the rod, 0.15 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 2.5 kgL = 1 md = 0.15 m
IO = kg·m²
2.Easy
Or = 0.05 mL = 0.7 m0.75 m3 kg4 kg

A pendulum is made of a uniform slender rod (3 kg, 0.7 m long) pivoted at its top end O, with a thin solid disc of mass 4 kg and radius 0.05 m fixed to its lower end. The disc swings in its own plane and its centre is 0.75 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 3 kgL = 0.7 mmdisc = 4 kgr = 0.05 md = 0.75 m
IO = kg·m²
3.Medium
14.5 kgaαM = 15 kgR = 0.15 m

A 14.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 15 kg and radius 0.15 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the tension T in the cord.

m = 14.5 kgM = 15 kgR = 0.15 mg = 9.81 m/s²
T = N
4.Medium
3.5 kgaαM = 7.5 kgR = 0.25 m

A 3.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 7.5 kg and radius 0.25 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the acceleration a of the block.

m = 3.5 kgM = 7.5 kgR = 0.25 mg = 9.81 m/s²
a = m/s²
5.Hard
10 m/sω

A thin hoop of mass 14.5 kg rolls without slipping at 10 m/s. What percentage p of its total kinetic energy is rotational?

m = 14.5 kgv = 10 m/sI = m·r²
p = %
6.Hard
θ = 25°a

A solid sphere rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 25°I = (2/5)·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 0.2646 kg·m²
  2. 2. IO = 2.745 kg·m²
  3. 3. T = 48.49 N
  4. 4. a = 4.736 m/s²
  5. 5. p = 50 %
  6. 6. μs = 0.1332

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