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 = 1.3 mGOd = 0.35 mm = 8 kg

A uniform slender rod of mass 8 kg and length 1.3 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 = 8 kgL = 1.3 md = 0.35 m
IO = kg·m²
2.Easy
k = 0.5 mn = 1400 rpm160 kg

A flywheel of mass 160 kg has a radius of gyration of 0.5 m about its axis. It spins at 1400 rpm. Find its kinetic energy Ek in kJ.

M = 160 kgk = 0.5 mn = 1400 rpm
Ek = kJ
3.Medium
v = ?4.5 kgL = 2.4 mm = 6.5 kg

A uniform slender rod of mass 6.5 kg and length 2.4 m is pinned at one end and released from rest in a horizontal position. A small ball of mass 4.5 kg is fixed to its free end. Ignore friction and use g = 9.81 m/s². Find the speed v of the free end as the rod swings through the vertical position.

m = 6.5 kgL = 2.4 mmball = 4.5 kgg = 9.81 m/s²
v = m/s
4.Medium
L = 3 mm = 18 kgα

A uniform slender rod of mass 18 kg and length 3 m is pinned at one end and held horizontal. It is released from rest. Use g = 9.81 m/s². Find the acceleration atip of the free end just after release.

m = 18 kgL = 3 mg = 9.81 m/s²
atip = m/s²
5.Hard
0.6 m0.2 mn1​ = 25 rpm

A person stands on a frictionless turntable and holds a 4 kg dumbbell in each hand, 0.6 m from the axis. The person and turntable alone have a moment of inertia of 5 kg·m² about the axis. They turn at 25 rpm, then pull the dumbbells in to 0.2 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 5 kg·m²m = 2 × 4 kgr1 = 0.6 mr2 = 0.2 mn1 = 25 rpm
n2 = rpm
6.Hard
θ = 25°as = 2.5 m

A thin hoop rolls without slipping down a slope inclined at 25° to the horizontal. Use g = 9.81 m/s². It starts from rest. How long t does it take to roll 2.5 m down the slope?

θ = 25°I = m·r²g = 9.81 m/s²s = 2.5 m
t = s

Answer key

  1. 1. IO = 2.107 kg·m²
  2. 2. Ek = 429.9 kJ
  3. 3. v = 7.399 m/s
  4. 4. atip = 14.71 m/s²
  5. 5. n2 = 37.03 rpm
  6. 6. t = 1.553 s

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