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
k = 0.3 m100 → 1700 rpm170 kg

A flywheel of mass 170 kg with a radius of gyration of 0.3 m is accelerated uniformly from 100 rpm to 1700 rpm. This takes 22 s. Ignoring friction, find the constant torque T needed.

m = 170 kgk = 0.3 mn1 = 100 rpmn2 = 1700 rpmt = 22 s
T = N·m
2.Easy
k = 0.55 m300 → 1700 rpm150 kg

A flywheel of mass 150 kg with a radius of gyration of 0.55 m is accelerated uniformly from 300 rpm to 1700 rpm. This takes 19 s. Ignoring friction, find the constant torque T needed.

m = 150 kgk = 0.55 mn1 = 300 rpmn2 = 1700 rpmt = 19 s
T = N·m
3.Medium
L = 1.3 mm = 2 kgα

A uniform slender rod of mass 2 kg and length 1.3 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 = 2 kgL = 1.3 mg = 9.81 m/s²
α = rad/s²
4.Medium
ω = ?2 kgL = 0.9 mm = 2.5 kg

A uniform slender rod of mass 2.5 kg and length 0.9 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 2 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 = 2.5 kgL = 0.9 mmball = 2 kgg = 9.81 m/s²
ω = rad/s
5.Hard
5 m/sω

A hollow sphere of mass 1 kg rolls without slipping at 5 m/s. Find its total kinetic energy Ek.

m = 1 kgv = 5 m/sI = (2/3)·m·r²
Ek = J
6.Hard
420 m/s25 g0.4 mL = 0.5 m5 kg

A uniform slender rod of mass 5 kg and length 0.5 m hangs at rest from a frictionless pivot at its top end. A 25 g bullet moving horizontally at 420 m/s hits the rod 0.4 m below the pivot and stays embedded. Find the angular velocity ω of the rod just after the impact.

M = 5 kgL = 0.5 mm = 25 gv = 420 m/sd = 0.4 m
ω = rad/s

Answer key

  1. 1. T = 116.5 N·m
  2. 2. T = 350.1 N·m
  3. 3. α = 11.32 rad/s²
  4. 4. ω = 5.001 rad/s
  5. 5. Ek = 20.83 J
  6. 6. ω = 9.984 rad/s

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