1. The problem statement, all variables and given/known data Consider a circular disc (that might be a tautology), free to rotate and translate in the xy-plane only. It has radius R, but its mass is unhomogeneously distributed in some unknown fashion. All we know is that the center of mass is displaced from the centre of the disc by some distance a, and that it has mass m. We can model a disc with such a center of mass by superimposing a disc and a point mass on its edge. After finding expressions for their masses in terms of m and a/R, some algebraic manipulation, and summing the respective known-from-theorem moments of inertia for the two ideal objects, we arrive at the moment of inertia for rotation around the center... 2. Relevant equations I = m * (1/2) * R^2 * (1 + a/R). 3. The attempt at a solution So, we get a moment of inertia that is a weighted mean between that of a disc and a point mass orbiting at distance R. My intuition is that under these constraints, this is the MoI for ALL circular discs characterized by radius R, displaced CoM ratio a/R, and mass m. I feel like there should be a relatively simple argument that shows this, that as long as the shape and radius of the object and the CoM remain the same, the rest of the mass distribution doesn't matter under the provided constraints. But I can't think of one, and that is driving me crazy... Anyone here that could help?