I have a rigid disk rotating around an external axis of rotation ( not even touching the disk ) , i tried to draw roughly the figure . The disk is not rotating around itself only the vertical axis passing through A . So what is the moment of inertia of the disk with respect to axis of rotation passing A ??

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You do not have a disc rotating around a single axis.

Rather you have a collection of individual points, all fixed relative to one another, in both distance and relative direction. Each point is moving in its own circle about a different axis; all the circles have the same radius.

The moment of inertia of a point mass is simple; moments of inertia for a collection of points are additive.


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