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 = 1.5 mGOd = 0.65 mm = 10.5 kg

A uniform slender rod of mass 10.5 kg and length 1.5 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 = 10.5 kgL = 1.5 md = 0.65 m
IO = kg·m²
2.Easy
Or = 0.1 mL = 1.4 m1.5 m1.5 kg5 kg

A pendulum is made of a uniform slender rod (1.5 kg, 1.4 m long) pivoted at its top end O, with a solid sphere of mass 5 kg and radius 0.1 m fixed to its lower end. The centre of the sphere is 1.5 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 1.5 kgL = 1.4 mmsphere = 5 kgr = 0.1 md = 1.5 m
IO = kg·m²
3.Medium
n = 1400 rpmTb​ = 200 N·mI = 17.5 kg·m²

A flywheel with a moment of inertia of 17.5 kg·m² spins at 1400 rpm. A brake applies a constant friction torque of 200 N·m. How long t does it take to stop?

I = 17.5 kg·m²n = 1400 rpmTb = 200 N·m
t = s
4.Medium
5 kgaαM = 19 kgR = 0.4 m

A 5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 19 kg and radius 0.4 m that turns on a frictionless horizontal axle. The block is released from rest. Use g = 9.81 m/s². Find the speed v of the block after it has fallen 2.5 m.

m = 5 kgM = 19 kgR = 0.4 mg = 9.81 m/s²h = 2.5 m
v = m/s
5.Hard
5 m/sω

A hollow sphere of mass 8 kg rolls without slipping at 5 m/s. What percentage p of its total kinetic energy is rotational?

m = 8 kgv = 5 m/sI = (2/3)·m·r²
p = %
6.Hard
θ = 10°a

A hollow sphere rolls without slipping down a slope inclined at 10° to the horizontal. Use g = 9.81 m/s². Find the smallest coefficient of static friction μs that prevents it from slipping.

θ = 10°I = (2/3)·m·r²g = 9.81 m/s²
μs =

Answer key

  1. 1. IO = 6.405 kg·m²
  2. 2. IO = 12.25 kg·m²
  3. 3. t = 12.83 s
  4. 4. v = 4.113 m/s
  5. 5. p = 40 %
  6. 6. μs = 0.07053

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