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i have to give a presentation on an example of the defining equation for the moment of inertia of a thin spherical shell. I have to follow the example in my book "elements of newtonian mechanics". I get most of it but there are a couple steps that the book skips that i cannot. I was wondering if anyone could better explain whats happening to me.

There is a thin spherical shell of mass M and radius R which is symetrically identical in the x, y and z coordinate system.

Ix = Iy = Iz

now Ix = integral (y^2 + z^2)dM i dont get this step.

R^2 = x^2 but i dont get the geometry of why x^2 = y^2 + z^2

Iy = integral (z^2 + x ^2)dM etc

now it says Itotal = 1/3(Ix + Iy + iz)

where does the 1/3 come from. Is it just taking the average or does it have to do with the parrallel axis theorem?

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# Homework Help: Moment of inertia of spherical shell

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