I need to derive the moment of inertia for a solid sphere, but I'm having some trouble. I did the following. I=?r^2dm given density, p= m/V pV=m so pdV=dm and differentiating V wrt r, d(4/3?r^3)dr = 4?r^2 so p4?r^2dr=dm and plugging that in I get I=?r^2(p4?r^2)dr I pull the p4? out in front I=p4??r^4dr evaluating the integral I get I=(M/(4/3?r^3))4?(r^5/5) simplifying the terms I get I=3/5mr^2 which is a universe off from what the answer should be, if anyone can show me where I went wrong I would be very appreciative. Thanks.