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 = 0.8 mGOd = 0.4 mm = 9 kg

A uniform slender rod of mass 9 kg and length 0.8 m rotates about an axis O perpendicular to the rod, 0.4 m from its centre G. Find its mass moment of inertia IO about that axis.

m = 9 kgL = 0.8 md = 0.4 m
IO = kg·m²
2.Easy
k = 0.3 m0 → 800 rpm110 kg

A flywheel of mass 110 kg with a radius of gyration of 0.3 m is accelerated uniformly from rest to 800 rpm. This takes 4 s. Ignoring friction, find the constant torque T needed.

m = 110 kgk = 0.3 mn1 = 0 rpmn2 = 800 rpmt = 4 s
T = N·m
3.Medium
L = 0.7 mm = 11 kgα

A uniform slender rod of mass 11 kg and length 0.7 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find its angular acceleration α just after release.

m = 11 kgL = 0.7 mg = 9.81 m/s²
α = rad/s²
4.Medium
1 kgaαM = 1 kgR = 0.5 m

A 1 kg block hangs from a light cord wrapped around a pulley, a uniform solid disc of mass 1 kg and radius 0.5 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 = 1 kgM = 1 kgR = 0.5 mg = 9.81 m/s²
α = rad/s²
5.Hard
560 m/s15 g0.32 mL = 0.8 m10 kg

A uniform slender rod of mass 10 kg and length 0.8 m hangs at rest from a frictionless pivot at its top end. A 15 g bullet moving horizontally at 560 m/s hits the rod 0.32 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 10 kgL = 0.8 mm = 15 gv = 560 m/sd = 0.32 m
ω = rad/s
6.Hard
0.7 m0.25 mn1​ = 20 rpm

A person stands on a frictionless turntable and holds a 3.5 kg dumbbell in each hand, 0.7 m from the axis. The person and turntable alone have a moment of inertia of 1.5 kg·m² about the axis. They turn at 20 rpm, then pull the dumbbells in to 0.25 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 1.5 kg·m²m = 2 × 3.5 kgr1 = 0.7 mr2 = 0.25 mn1 = 20 rpm
n2 = rpm

Answer key

  1. 1. IO = 1.92 kg·m²
  2. 2. T = 207.3 N·m
  3. 3. α = 21.02 rad/s²
  4. 4. α = 13.08 rad/s²
  5. 5. ω = 1.259 rad/s
  6. 6. n2 = 50.89 rpm

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