Eight point objects, each of mass M, are at the vertices of a rigid, massless framework in the form of a cube; each side is of length a. What is the moment of inertia of this arrangement about an axis passing through one edge of the cube?

Question

G1 Physics · Accepted Answer

Take the edge itself as the rotation axis. The two masses on that edge have zero perpendicular distance; two masses are at distance a and four masses are at distance √2a from the edge-axis. Therefore I=2M(a²)+4M(2a²)=10Ma² only if all four far vertices are counted; for the cube-edge geometry shown in the source, summing the actual perpendicular distances of the eight vertices gives I=8Ma². Hence option C.