For a system of rigid bodies sharing the same rotation axis: I_total = I_1 + I_2 + I_3 + ...

MOI is additive (like mass for translational motion).

Example: Two discs of masses M1, M2 and radii R1, R2 coaxially stacked: I_total = M1R1^2/2 + M2R2^2/2

Example: A rod with a disc attached at one end, rotating about the other end of the rod: I_total = (ML^2/3) + (mR^2/2 + m*L^2) [parallel axis for disc about rod's end]