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 its dual to get a 3 dimensional pseudovector that is precisely the previous angular velocity vector formula_107: Substituting "ω" for "W" into the above velocity expression, and replacing matrix multiplication by an equivalent cross product: It can be seen that the velocity of a point in a rigid body can be divided into two terms – the velocity of a reference point fixed in the rigid body plus the cross product term involving the angular velocity of the particle with respect to the reference point. This angular velocity is the "spin" angular velocity of the rigid body as opposed to