Hi all, You can use superposition to add moments of inertia when they're calculated about the same center of gravity (cg), but let's say you calculate the moments of inertia of several elements of a system about one cg and then use the Parallel Axis Theorem to then reference the total moments for these elements back to the total system cg. Do you get the same answer? I had assumed yes, but then did some math that's making me not so sure. Most basic example: Let's say I have 3 mass elements in a 3 dimensional space. I am given the mass and cgs (relative to a reference frame origin) of each element, as well as the moment of inertia of each element about its own cg. I lump together two of the elements and treat this as a new element. I find the mass, cg_lumped, and moments of this new lumped element relative to cg_lumped. Next, I want to find the TOTAL moments of inertia of the lumped element plus the 3rd element relative to the total system cg - call it cg_total. I end up with extra terms using the "lumped method." I guess it's nonlinear... I may have messed up my math and there may be a cleaner way to do it, but I just want a proof one way or another of whether the answer would be the same in general. My math focuses on the Ixx (inertia about the X axis through the cg) only. Setup and math here Thank you! Alexa.