Let be the original disk centre and the hole centre. The source geometry has , , all collinear. The removed disk has mass , since its area is one quarter of the original disk's. Use the parallel axis theorem for both the original disk and the removed disk:
(1)
Subtracting the missing material's moment of inertia gives
(2)
Here continues to denote the original unperforated disk mass; the earring itself has mass .
Figure 1.
Equilibrium geometry and mass subtraction for a perforated-disk physical pendulum
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