A description of how mass is assigned to positions, expressed for example by point masses, a mass density, or a measure. Writing allows centre of mass and moment of inertia formulas to cover both discrete and continuous cases.
A planar lamina is an ideal mass distribution confined to a plane, with surface mass density and infinitesimal mass . Its moment of inertia about an axis is the integral of squared perpendicular distance against this mass element. Three mutually perpendicular axes through one point, with two in the lamina's plane, obey the perpendicular axis theorem even when the density is nonuniform.
