Calculating the Density Function for Redistribution of Melted Ice on Earth

[metgt4]

Hey Everybody,

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

 

[ideasrule]

If the mass is distributed evenly, it would be a shell of uniform thickness surrounding the Earth. Since this shell is very thin compared to Earth's radius, you can compute its moment of inertia using I=2/3*MR^2, valid for a thin shell.

 

[metgt4]

Oh, man, I must REALLY need some sleep! I just got in the routine of estimating everything as a disc rotating around the axis. Thanks for pointing me in the right direction there.