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 = 0.5 mGOd = 0.15 mm = 4 kg

A uniform slender rod of mass 4 kg and length 0.5 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 = 4 kgL = 0.5 md = 0.15 m
IO = kg·m²
2.Easy
L = 1.8 mGOd = 0.45 mm = 1 kg

A uniform slender rod of mass 1 kg and length 1.8 m rotates about an axis O perpendicular to the rod, 0.45 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 1 kgL = 1.8 md = 0.45 m
IO = kg·m²
3.Medium
ω = ?4 kgL = 2.4 mm = 5 kg

A uniform slender rod of mass 5 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4 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 = 2.4 mmball = 4 kgg = 9.81 m/s²
ω = rad/s
4.Medium
n = 1800 rpmTb​ = 15 N·mI = 39 kg·m²

A flywheel with a moment of inertia of 39 kg·m² spins at 1800 rpm. A brake applies a constant friction torque of 15 N·m. How long t does it take to stop?

I = 39 kg·m²n = 1800 rpmTb = 15 N·m
t = s
5.Hard
540 m/s5 g0.44 mL = 0.6 m4 kgφ

A uniform slender rod of mass 4 kg and length 0.6 m hangs at rest from a frictionless pivot at its top end. A 5 g bullet moving horizontally at 540 m/s hits the rod 0.44 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 = 4 kgL = 0.6 mm = 5 gv = 540 m/sd = 0.44 mg = 9.81 m/s²
φ = °
6.Hard
3 m/sω

A solid sphere of mass 17 kg rolls without slipping at 3 m/s. What percentage p of its total kinetic energy is rotational?

m = 17 kgv = 3 m/sI = (2/5)·m·r²
p = %

Answer key

  1. 1. IO = 0.1733 kg·m²
  2. 2. IO = 0.4725 kg·m²
  3. 3. ω = 3.062 rad/s
  4. 4. t = 490.1 s
  5. 5. φ = 28.88 °
  6. 6. p = 28.57 %

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