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So if I wanted to calculate the potential energy between two points on a disk, would I just use the formula for Gravitational Potential energy? if so, what would be the mass? Would I use some form of moment of Inertia to calculate it?

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A point on a disk has zero mass and therefore two points have no gravitational potential energy. However you can calculate the PE between two infinitesimal volume (or area, if the disk is infinitely thin) elements with infinitesimal masses, using the usual formula. The point of doing this is then to doubly-integrate over the entire object to get its PE as the sum of the PEs of its parts.

The moment of inertia has nothing to do with gravitational potential energy. However, calculating the moment of inertia of a solid body, and calculating the gravitational potential or potential energy of a solid body, both involve treating the sold body as an infinite collection of infinitesimal masses.

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