Relativistic angular momentum can be compactly abbreviated in tensor index notation where the indices "i" and "j" take the values 1, 2, 3. On the other hand, the components can be systematically displayed fully in a 3 × 3 antisymmetric matrix This quantity is additive, and for an isolated system, the total angular momentum of a system is conserved. In classical mechanics, the three-dimensional quantity for a particle of mass "m" moving with velocity u has the dimensions of "mass moment" – length multiplied by mass. It is related to the boost (relative velocity) of the centre of mass (COM) of the particle
Mass in special relativity geometry of Minkowski-space, the velocity-space is bounded by "c" and has the geometry of hyperbolic geometry where relativistic-mass plays an analogous role to that of Newtonian-mass in the barycentric-coordinates of Euclidean geometry. The connection of velocity to hyperbolic-geometry enables the 3-velocity-dependent relativistic-mass to be related to the 4-velocity Minkowski-formalism. Mass in special relativity Mass in special relativity incorporates the general understandings from the laws of motion of special relativity along with its concept of mass–energy equivalence. The word "mass" is given two meanings in special relativity: one ("rest" or "invariant mass", and its equivalent "rest energy") is an invariant quantity