Massefordeling

Massefordeling, or mass distribution, describes how mass is arranged within an object or system. It affects the location of the center of mass, rotational properties, and the response to external forces. Mass distribution can be described by density functions: in one dimension a linear density λ(x); in two dimensions a surface density σ(x,y); and in three dimensions a volume density ρ(x,y,z). The total mass is M = ∫ ρ dV.

The center of mass R_cm is defined as R_cm = (1/M) ∫ r ρ dV for continuous bodies, and, for a set of discrete particles, R_cm = ∑ m_i r_i / ∑ m_i. If density is uniform, R_cm coincides with the geometric center; for non-uniform distributions it shifts toward regions with greater mass.

Moments of inertia I quantify how mass is distributed relative to an axis and determine rotational resistance: I = ∫ r^2 dm for a given axis. Different distributions yield different inertia values, even when total mass is the same.

Common cases include uniform bodies, where symmetry simplifies calculations, and non-uniform bodies, where density variations must be integrated. Engineers use mass distribution to assess stability, load paths, and dynamic behavior in structures, vehicles, and machinery.

Determination can be analytical, using density functions, or experimental, via balance tests, imaging methods, or finite element modeling. Understanding mass distribution also informs gravitational and geophysical models of planetary bodies.

See also center of gravity, barycenter, density, and moment of inertia.