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(I/M)) provides a convenient single-number description of mass distribution for rolling problems.