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–energy equivalence the velocity is small, the relativistic mass and the rest mass are almost exactly the same. Also Einstein (following Hendrik Lorentz and Max Abraham) used velocity- and direction-dependent mass concepts () in his 1905 electrodynamics paper and in another paper in 1906. However, in his first paper on (1905), he treated as what would now be called the "rest mass". Some claim that (in later years) he did not like the idea of "relativistic mass". When modern physicists say "mass", they are usually talking about rest mass, since if they meant "relativistic mass", they would just say "energy". Considerable debate