Moment of inertia is not a single number for a body — it depends on the axis of rotation. The same body has different MOI about different axes, with the minimum always through the centre of mass (parallel axis theorem guarantees $I_{cm}$ is the minimum among parallel axes).

For composite bodies, MOI is additive: $I_{total}$ = $I_1$ + $I_2$ + ... For bodies with holes, subtract: $I_{remaining}$ = $I_{full}$ - $I_{removed}$. When the removed portion's CM is not on the chosen axis, use the parallel axis theorem to shift it before subtracting.

The perpendicular axis theorem ($I_z$ = $I_x$ + $I_y$) is a powerful shortcut for 2D bodies. For example, a disc's MOI about a diameter is obtained from: $I_z$ = 2*$I_{diameter}$, giving $I_{diameter}$ = $MR^2$/4. This theorem CANNOT be applied to 3D bodies like spheres or cylinders.

Radius of gyration (k = sqrt$\frac{I}{M}$) provides a convenient single-number description of mass distribution for rolling problems.