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 = 2.7 mGOd = 0.85 mm = 5 kg

A uniform slender rod of mass 5 kg and length 2.7 m rotates about an axis O perpendicular to the rod, 0.85 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 5 kgL = 2.7 md = 0.85 m
IO = kg·m²
2.Easy
Or = 0.1 mL = 0.6 m0.7 m4.5 kg8.5 kg

A pendulum is made of a uniform slender rod (4.5 kg, 0.6 m long) pivoted at its top end O, with a thin solid disc of mass 8.5 kg and radius 0.1 m fixed to its lower end. The disc swings in its own plane and its centre is 0.7 m below O. Find the mass moment of inertia IO of the pendulum about O.

mrod = 4.5 kgL = 0.6 mmdisc = 8.5 kgr = 0.1 md = 0.7 m
IO = kg·m²
3.Medium
5.5 kgaαM = 20 kgR = 0.4 m

A 5.5 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 20 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 tension T in the cord.

m = 5.5 kgM = 20 kgR = 0.4 mg = 9.81 m/s²
T = N
4.Medium
n = 600 rpmTb​ = 195 N·mI = 7 kg·m²

A flywheel with a moment of inertia of 7 kg·m² spins at 600 rpm. A brake applies a constant friction torque of 195 N·m. How long t does it take to stop?

I = 7 kg·m²n = 600 rpmTb = 195 N·m
t = s
5.Hard
340 m/s35 g0.6 mL = 1 m7 kgφ

A uniform slender rod of mass 7 kg and length 1 m hangs at rest from a frictionless pivot at its top end. A 35 g bullet moving horizontally at 340 m/s hits the rod 0.6 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 = 7 kgL = 1 mm = 35 gv = 340 m/sd = 0.6 mg = 9.81 m/s²
φ = °
6.Hard
9.5 m/sω

A solid cylinder of mass 1.5 kg rolls without slipping at 9.5 m/s. Find its total kinetic energy Ek.

m = 1.5 kgv = 9.5 m/sI = ½·m·r²
Ek = J

Answer key

  1. 1. IO = 6.65 kg·m²
  2. 2. IO = 4.747 kg·m²
  3. 3. T = 34.81 N
  4. 4. t = 2.256 s
  5. 5. φ = 46.73 °
  6. 6. Ek = 101.5 J

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