Nonrotating Local Frame

APPENDIX G FORCES, ENERGY, AND WORK G.7 Nonrotating Local Frame... 

Consider the case of a nonrotating local frame whose origin moves in the lab frame but whose Cartesian axes x, y, z remain parallel to the axes x, z of the lab frame. In this case the Cartesian components of F/ for particle i are the same in both frames, and so also are the Cartesian components of the infinitesimal vector displacement driz. According to Eqs. G.4.4 and G.6.8, then, for an arbitrary process the value of the heat q in the local frame is the same as the value of the heat qi b in the lab frame. 

If we use a center-of-mass frame (cm frame) for the local frame, the internal energy change during a process is related in a particularly simple way to the system energy change measured in a lab frame. A cm frame has its origin at the center of mass of the system and its Cartesian axes parallel to the Cartesian axes of a lab frame. This is a special case of the nonrotating local frame discussed in Sec. G.7. Since the center of mass may accelerate in the lab frame, a cm frame is not necessarily inertial. 

Only by using a nonrotating local frame moving with the center of mass is it possible to derive such a simple relation among these kinetic energy quantities. 

With these substitutions, Eq. G.8.6 becomes AU — AEsys = —jmA(v ) — mgAzcm-Since AU — AEsys is equal to u — wiab when the local frame is nonrotating (Eq. G.7.1), we have... 

In a rotating local frame, the work during a process is not the same as that measured in a lab frame. The heats q and are not equal to one another as they are when the local frame is nonrotating, nor can general expressions using macroscopic quantities be written... 

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