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Let's say I have a body consisting of two homogenous spheres/balls that touch each other. I also have a body fixed coordinate system which consists of that body's principal axes. I know the the moment of inertia for each of the spheres alone, $I=\frac{2}{5}mr^2$. Can I use that to find the moment of inertia of the entire body?

I need this because for such a body, with such a coordinate system, I don't think integration would be very simple...

I'm looking for all three moment of inertias, however two of them should be the same because of rotational symmetry.

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up vote 1 down vote accepted

about the axis passing two centers: $I=\frac{2}{5}mR^2+\frac{2}{5}mR^2$

about each of two axes perpendicular to each other and previous one passing the contact point : $I=\frac{2}{5}mR^2+mR^2+\frac{2}{5}mR^2+mR^2$ (using parallel axes theorem)

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