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
k = 0.3 mn = 2900 rpm100 kg

A flywheel of mass 100 kg has a radius of gyration of 0.3 m about its axis. It spins at 2900 rpm. Find its kinetic energy Ek in kJ.

M = 100 kgk = 0.3 mn = 2900 rpm
Ek = kJ
2.Easy
L = 2.6 mGOd = 0.3 mm = 4.5 kg

A uniform slender rod of mass 4.5 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.3 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 4.5 kgL = 2.6 md = 0.3 m
IO = kg·m²
3.Medium
ω = ?1.5 kgL = 2.3 mm = 5 kg

A uniform slender rod of mass 5 kg and length 2.3 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 1.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the angular velocity ω of the rod as it swings through the vertical position.

m = 5 kgL = 2.3 mmball = 1.5 kgg = 9.81 m/s²
ω = rad/s
4.Medium
L = 2.4 mm = 13 kgα

A uniform slender rod of mass 13 kg and length 2.4 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 = 2.4 mg = 9.81 m/s²
atip = m/s²
5.Hard
300 m/s30 g0.83 mL = 1.2 m8 kgφ

A uniform slender rod of mass 8 kg and length 1.2 m hangs at rest from a frictionless pivot at its top end. A 30 g bullet moving horizontally at 300 m/s hits the rod 0.83 m below the pivot and stays embedded. Use g = 9.81 m/s². Find the largest angle φ from the vertical through which the rod swings.

M = 8 kgL = 1.2 mm = 30 gv = 300 m/sd = 0.83 mg = 9.81 m/s²
φ = °
6.Hard
1 m/sω

A solid cylinder of mass 16 kg rolls without slipping at 1 m/s. What percentage p of its total kinetic energy is rotational?

m = 16 kgv = 1 m/sI = ½·m·r²
p = %

Answer key

  1. 1. Ek = 415 kJ
  2. 2. IO = 2.94 kg·m²
  3. 3. ω = 3.283 rad/s
  4. 4. atip = 14.71 m/s²
  5. 5. φ = 32.08 °
  6. 6. p = 33.33 %

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