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-to-charge ratio used as its unit in the field of mass spectrometry. Some fields use the charge-to-mass ratio ("Q"/"m") instead, which is the multiplicative inverse of the mass-to-charge ratio. The 2014 CODATA recommended value for an electron is = . When charged particles move in electric and magnetic fields the following two laws apply: where F is the force applied to the ion, "m" is the mass of the particle, a is the acceleration, "Q" is the electric charge, E is the electric field, and v × B is the cross product of the ion's velocity and the magnetic flux density. This