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 = 0.4 mn = 1500 rpm300 kg

A flywheel is a uniform solid disc of mass 300 kg and radius 0.4 m. It spins at 1500 rpm. Find its kinetic energy Ek in kJ.

M = 300 kgR = 0.4 mn = 1500 rpm
Ek = kJ
2.Easy
R = 0.4 mn = 1700 rpm90 kg

A flywheel is a uniform solid disc of mass 90 kg and radius 0.4 m. It spins at 1700 rpm. Find its kinetic energy Ek in kJ.

M = 90 kgR = 0.4 mn = 1700 rpm
Ek = kJ
3.Medium
2.5 kgaαM = 1 kgR = 0.4 m

A 2.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 1 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 4.5 m.

m = 2.5 kgM = 1 kgR = 0.4 mg = 9.81 m/s²h = 4.5 m
v = m/s
4.Medium
v = ?0.5 kgL = 0.9 mm = 8 kg

A uniform slender rod of mass 8 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 0.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 8 kgL = 0.9 mmball = 0.5 kgg = 9.81 m/s²
v = m/s
5.Hard
4 m/sω

A hollow sphere of mass 5.5 kg rolls without slipping at 4 m/s. What percentage p of its total kinetic energy is rotational?

m = 5.5 kgv = 4 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 acceleration a of its centre.

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

Answer key

  1. 1. Ek = 296.1 kJ
  2. 2. Ek = 114.1 kJ
  3. 3. v = 8.578 m/s
  4. 4. v = 5.009 m/s
  5. 5. p = 40 %
  6. 6. a = 1.022 m/s²

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