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
R = 0.4 mn = 1000 rpm190 kg

A flywheel is a uniform solid disc of mass 190 kg and radius 0.4 m. It spins at 1000 rpm. Find its kinetic energy Ek in kJ.

M = 190 kgR = 0.4 mn = 1000 rpm
Ek = kJ
2.Easy
k = 0.55 mn = 1900 rpm250 kg

A flywheel of mass 250 kg has a radius of gyration of 0.55 m about its axis. It spins at 1900 rpm. Find its kinetic energy Ek in kJ.

M = 250 kgk = 0.55 mn = 1900 rpm
Ek = kJ
3.Medium
ω = ?L = 2.2 mm = 5.5 kg

A uniform slender rod of mass 5.5 kg and length 2.2 m is pinned at one end and released from rest in a horizontal position. 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 = 5.5 kgL = 2.2 mg = 9.81 m/s²
ω = rad/s
4.Medium
L = 2.7 mm = 9.5 kgα

A uniform slender rod of mass 9.5 kg and length 2.7 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 = 9.5 kgL = 2.7 mg = 9.81 m/s²
atip = m/s²
5.Hard
3.5 m/sω

A solid sphere of mass 12 kg rolls without slipping at 3.5 m/s. What percentage p of its total kinetic energy is rotational?

m = 12 kgv = 3.5 m/sI = (2/5)·m·r²
p = %
6.Hard
0.8 m0.35 mn1​ = 40 rpm

A person stands on a frictionless turntable and holds a 1.5 kg dumbbell in each hand, 0.8 m from the axis. The person and turntable alone have a moment of inertia of 4.5 kg·m² about the axis. They turn at 40 rpm, then pull the dumbbells in to 0.35 m from the axis. Treat the dumbbells as point masses. Find the new speed n2 in rpm.

I0 = 4.5 kg·m²m = 2 × 1.5 kgr1 = 0.8 mr2 = 0.35 mn1 = 40 rpm
n2 = rpm

Answer key

  1. 1. Ek = 83.34 kJ
  2. 2. Ek = 1497 kJ
  3. 3. ω = 3.657 rad/s
  4. 4. atip = 14.71 m/s²
  5. 5. p = 28.57 %
  6. 6. n2 = 52.76 rpm

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