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Right now I'm working on a what would happen to the moment of inertia if all of the ice on earth melted and were to be redistributed. I've found the moment of inertia of all of the grounded ice on earth and the moment of inertia of the earth without this ice, but now I need to redistribute this mass evenly over the surface of the earth. I know that the moment of inertia of this redistribution could be shown as a disc of infinitesimal thickness at the equator, but the mass distribution would be less at the centre of this disc and increase as you got further and further from the centre. How would you go about finding the density function in this problem? This one has me stumped!

Thanks!

Andrew