Why perpendicular axis theorem is not applicable for spheres?
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If you go through the proof for perpendicular axis theorem, there is a step where you set ∫x^2dm=Iy ; ∫y^2dm=Ix.
This is true only for a planar object in the x-y plane.
For general 3D objects, the equation reads
∫(x^2+z^2)dm=Iy ; ∫(y^2+z^2)dm=Ix
That is, perpendicular axis theorem doesn't work for 3D objects because it is derived under the assumption that the object is planar.
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