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 = 0.2 mm = 8 kg

A uniform slender rod of mass 8 kg and length 0.5 m rotates about an axis O perpendicular to the rod, 0.2 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 8 kgL = 0.5 md = 0.2 m
IO = kg·m²
2.Easy
L = 2.6 mGOd = 0.35 mm = 11.5 kg

A uniform slender rod of mass 11.5 kg and length 2.6 m rotates about an axis O perpendicular to the rod, 0.35 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 11.5 kgL = 2.6 md = 0.35 m
IO = kg·m²
3.Medium
n = 1000 rpmTb​ = 120 N·mI = 9 kg·m²

A flywheel with a moment of inertia of 9 kg·m² spins at 1000 rpm. A brake applies a constant friction torque of 120 N·m. How many revolutions N does the flywheel make before it stops?

I = 9 kg·m²n = 1000 rpmTb = 120 N·m
N = rev
4.Medium
6 kgaαM = 5.5 kgR = 0.1 m

A 6 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 5.5 kg and radius 0.1 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 = 6 kgM = 5.5 kgR = 0.1 mg = 9.81 m/s²
α = rad/s²
5.Hard
disc: 34 kgring: 10 kgn1​ = 550 rpm

A uniform solid disc (mass 34 kg, radius 0.15 m) spins freely at 550 rpm about a vertical frictionless shaft. A thin ring of mass 10 kg and the same radius is dropped onto it from rest, centred on the shaft, and the two quickly spin together. Find their common speed n2 in rpm.

Mdisc = 34 kgMring = 10 kgR = 0.15 mn1 = 550 rpm
n2 = rpm
6.Hard
140 m/s45 g0.38 mL = 0.7 m8 kgφ

A uniform slender rod of mass 8 kg and length 0.7 m hangs at rest from a frictionless pivot at its top end. A 45 g bullet moving horizontally at 140 m/s hits the rod 0.38 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 = 0.7 mm = 45 gv = 140 m/sd = 0.38 mg = 9.81 m/s²
φ = °

Answer key

  1. 1. IO = 0.4867 kg·m²
  2. 2. IO = 7.887 kg·m²
  3. 3. N = 65.45 rev
  4. 4. α = 67.27 rad/s²
  5. 5. n2 = 346.3 rpm
  6. 6. φ = 22.92 °

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