Consider the frame of reference Ax?? y?? z?? in translation with respect to the Newtonian frame of reference Oxyz. We define the angular momentum H??A of a system of n particles about A as the sum of the moments about A of the moment a miv?? i of the particles in their motion relative to the frame Ax?? y?? z??. Denoting by HA the sum of the moments about A of the moment a mivi of the particles in their motion relative to the Newtonian frame Oxyz, show that HA = H??A at a given instant if, and only if, one of the following conditions is satisfied at that instant:

(a) A has zero velocity with respect to the frame Oxyz,

(b) A coincides with the mass center G of the system,

(c) The velocity Va relative to Oxyz is directed along the line AG.

Transcribed Image Text:

A M H = 21×mv i=] Η Σ1×m;" (2) i=1 HA || (1)