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So... I=r^2dm Assuming a const mass density: I=p r^2 dV, (p=mass/volume). For a sphere the natural choice of

dV = r^2 dr d(omega). So this leads to:

I=4(pi) p r^4 dr . Lets say that the sphere has a radius b.

Therefore: I=4(pi) p b^5/5, with p=m/(4/3 pi b^3)

This gives me a final answer of I=3/5 m b^2, which is according to ever text I have looked at (Serway, Halliday/Reznik) incorrect.

The supposed correct answer would be: I=2/5 m b^2

I should be able to do this but I seem to be unable to find the assumption that is leading to my error. Something is tickling the back of my mind from my undergrad years telling me there is a subtle point I am missing.

Any help would be greatly appreciated.