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 = 1.4 mGOd = 0.55 mm = 7.5 kg

A uniform slender rod of mass 7.5 kg and length 1.4 m rotates about an axis O perpendicular to the rod, 0.55 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 7.5 kgL = 1.4 md = 0.55 m
IO = kg·m²
2.Easy
k = 0.6 m0 → 1100 rpm140 kg

A flywheel of mass 140 kg with a radius of gyration of 0.6 m is accelerated uniformly from rest to 1100 rpm. This takes 3 s. Ignoring friction, find the constant torque T needed.

m = 140 kgk = 0.6 mn1 = 0 rpmn2 = 1100 rpmt = 3 s
T = N·m
3.Medium
ω = ?L = 0.6 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 0.6 m is pinned at one end and released from rest in a horizontal position. 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 = 5.5 kgL = 0.6 mg = 9.81 m/s²
ω = rad/s
4.Medium
L = 1.7 mm = 2.5 kgα

A uniform slender rod of mass 2.5 kg and length 1.7 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 = 2.5 kgL = 1.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
1.5 m/sω

A hollow sphere of mass 19.5 kg rolls without slipping at 1.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 19.5 kgv = 1.5 m/sI = (2/3)·m·r²
p = %
6.Hard
380 m/s20 g1.75 mL = 2 m8 kgφ

A uniform slender rod of mass 8 kg and length 2 m hangs at rest from a frictionless pivot at its top end. A 20 g bullet moving horizontally at 380 m/s hits the rod 1.75 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 = 2 mm = 20 gv = 380 m/sd = 1.75 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. IO = 3.494 kg·m²
  2. 2. T = 1935 N·m
  3. 3. ω = 7.004 rad/s
  4. 4. atip = 14.71 m/s²
  5. 5. p = 40 %
  6. 6. φ = 26.44 °

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