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For questions about problems related to physics that involve evaluating integrals. Purely mathematical questions should be asked at math.SE.

2 votes
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Center-of-mass and relative coordinate integral transformation

It looks like you have a pair of 3D integration variables in spherical coordinates, albeit ones in which you've integrated out the angular coordinates. …
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11 votes

Why doesn't this way of calculating the moment of inertia of a sphere work?

That's a good, well-stated question and the premise is indeed correct: your independent approach has failed. It fails because you're using $r$ for the distance of the mass of a spherical shell of radi …
David's user avatar
  • 703