The Local Frame and Internal Energy

As explained in Sec. 2.6.2, a lab frame may not be an appropriate reference frame in which to measure changes in the system s energy. This is the case when the system as a whole moves or rotates in the lab frame, so that Esys depends in part on external coordinates that are not state functions. In this case it may he possible to define a local frame moving with the system in which the energy of the system is a state function, the internal energy U. 

As before, r,- is the position vector of particle i in a lab frame. A prime notation will be used for quantities measured in the local frame. Thus the position of particle i relative to the local frame is given by vector rj, which points from the origin of the local frame to particle i (see Fig. G.3). The velocity of the particle in the local frame is = dr- / dt. 

We continue to treat the earth-fixed lab frame as an inertial frame, although this is not strictly true (Sec. G.IO). If the origin of the local frame moves at constant velocity in the lab frame, with Cartesian axes that do not rotate with respect to those of the lah frame, then the 

If the origin of the local frame moves with nonconstant velocity in the lab frame, or if the local frame rotates with respect to the lab frame, then the local frame has finite acceleration and is noninertial. In this case the motion of particle i in the local frame does not obey Newton s second law as it does in an inertial frame. We can, however, define an effective net force whose relation to the particle s acceleration in the local frame has the same form as Newton s second law  

To an observer who is stationary in the local frame, the effective force will appear to make the particle s motion obey Newton s second law even though the frame is not inertial. 

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APPENDIX G FORCES, ENERGY, AND WORK G.6 The Local Frame and Internal Energy... 

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