The Hydrodynamic Angular Momentum Equation

The law of conservation of angular momentum as applied to a system in which there is no intnnsic angular momentum is  

If we form the cross product of the position vector r with the hydrodynamic equation of motion in Eq. (7.1), the following equation is obtained  

We now turn to the molecular derivation of the equation of change for angular momentum The quantity [rf x pj ] is the angular momentum of a bead with respect to some arbitrarily chosen fixed reference frame. The beads are regarded as point particles, and hence possess no intrinsic angular momentum. Consequently, to obtain Eq. (9.1) from the statistical mechanical approach, we consider the following vector function B in the phase spaces = E K x p ] 5 (r - r) (9.4) 

Then B , which is the density of total angular momentum, is  

Hence the general equation of change in Eq. (3.7) gives Eq. (9.2) directly. 

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