I need to derive the moment of inertia for a solid sphere, but I'm having some trouble.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Derivation of solid sphere moment of inertia

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