Second moment of mass and energy for a torus using E=mc²

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colinbeaton1
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What could we learn if we found the second moment of mass for a taurus and use E = mc2 to find second moment of energy?
 
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We may be able to learn if a red rag has any effect ("taurus" means "bull") - perhaps you mean a "torus"? Sort of a doughnut shape?

The second moment of mass is just the moment of inertia.
So we know what that is.

E=mc^2 would be the rest-mass energy of something.
Just blindly substituting a rest-mass energy density for mass in the moment of inertia calculation will still get you the (non-relativistic) moment of inertia as before - just in different units.