Torque the vector cross product, p is the particle's linear momentum, and r is the displacement vector from the origin (the origin is assumed to be a fixed location anywhere in space). The time-derivative of this is: This result can easily be proven by splitting the vectors into components and applying the product rule. Now using the definition of force formula_17 (whether or not mass is constant) and the definition of velocity formula_18 The cross product of momentum formula_20 with its associated velocity formula_21 is zero because velocity and momentum are parallel, so the second term vanishes. By definition, torque τ
Mass–energy equivalence equivalence of mass and energy". In addition, Einstein used the formula , with being the energy of a system of mass points, to describe the energy and mass increase of that system when the velocity of the differently moving mass points is increased. In June 1907, Max Planck rewrote Einstein's mass–energy relationship as , where is the pressure and the volume to express the relation between mass, its "latent energy", and thermodynamic energy within the body. Subsequently, in October 1907, this was rewritten as and given a quantum interpretation by Johannes Stark, who assumed its validity and correctness ("Gültigkeit"). In