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The pendulum shown in the figure (see attachment) consists of a thin disk and two slender rods. The disk has a mass of 2 kg, the longer rod AB has a mass of 6.5 kg and the shorter rod CD has a mass of 2.5 kg. Determine the moment of inertia of the pendulum about an axis perpendicular to the page passing through (a) point O, and (b) the mass center G of the pendulum.

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Moment of inertia of the pendulum about axis passing through O = MI of the disc + MI of the rod AB + MI of the rod CD
MI of the disc about axis through O
We know that MI of the disc about an axis passing through its centre, perpendicular to the plane of the disc = IDisc1 = ½ MR2 where M = Mass of the disc, R = Radius
Substituting values we get: IDC = ½ x 2 x 0.22 = 0.04 kg.m2
By parallel axis theorem: MI of the disc about an axis passing O = IDO = IDC + M(AO)2 = 0.04 + 2 x (0.8 + 0.2)2 ...

Solution Summary

This solution shows how to find the moment of inertia of a pendulum.