Mass in special relativity what causes these particles to be termed "massless." However, even massless particles have a relativistic mass, which varies with their observed energy in various frames of reference, The invariant mass is the ratio of four-momentum (the four-dimensional generalization of classical momentum) to four-velocity: and is also the ratio of four-acceleration to four-force when the rest mass is constant. The four-dimensional form of Newton's second law is: The relativistic expressions for "E" and "p" obey the relativistic energy–momentum relation: where the m is the rest mass, or the invariant mass for systems, and "E" is the total energy. The equation is
Angular velocity two-dimensional case above, one may define the angular velocity vector as: where "θ" is the angle between r and v. In terms of the cross product, this is: From this, one can recover the tangential velocity as: If a point rotates with angular velocity formula_28 in a coordinate frame formula_29 which itself rotates with an angular velocity formula_30 with respect to an external frame formula_31, we can define formula_32 to be the composite angular velocity vector of the point with respect to formula_31. This operation coincides with usual addition of vectors, and it gives angular velocity the algebraic structure of