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 = 0.3 mn = 700 rpm260 kg

A flywheel is a uniform solid disc of mass 260 kg and radius 0.3 m. It spins at 700 rpm. Find its kinetic energy Ek in kJ.

M = 260 kgR = 0.3 mn = 700 rpm
Ek = kJ
2.Easy
L = 0.4 mGOd = 0.15 mm = 6 kg

A uniform slender rod of mass 6 kg and length 0.4 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 = 6 kgL = 0.4 md = 0.15 m
IO = kg·m²
3.Medium
5.5 kgaαM = 12.5 kgR = 0.2 m

A 5.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 12.5 kg and radius 0.2 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 = 5.5 kgM = 12.5 kgR = 0.2 mg = 9.81 m/s²
α = rad/s²
4.Medium
L = 0.6 mm = 13 kgα

A uniform slender rod of mass 13 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 = 13 kgL = 0.6 mg = 9.81 m/s²
atip = m/s²
5.Hard
460 m/s40 g0.56 mL = 1.4 m2 kg

A uniform slender rod of mass 2 kg and length 1.4 m hangs at rest from a frictionless pivot at its top end. A 40 g bullet moving horizontally at 460 m/s hits the rod 0.56 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 2 kgL = 1.4 mm = 40 gv = 460 m/sd = 0.56 m
ω = rad/s
6.Hard
θ = 35°as = 3.5 m

A hollow sphere rolls without slipping down a slope inclined at 35° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 3.5 m down the slope?

θ = 35°I = (2/3)·m·r²g = 9.81 m/s²s = 3.5 m
t = s

Answer key

  1. 1. Ek = 31.43 kJ
  2. 2. IO = 0.215 kg·m²
  3. 3. α = 22.96 rad/s²
  4. 4. atip = 14.71 m/s²
  5. 5. ω = 7.811 rad/s
  6. 6. t = 1.44 s

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