The §6.2 reading defines "relatively inertial reference frame" as follows: First, R is the vector from one frame's origin to another's. Then, A = d^2 R/dt^2. Finally, frames are "relatively inertial" if A=0.
But suppose I have two frames that share a common origin for all time, but that rotate with respect to one another. Then R is 0 for all time, so A=0. These frames thus satisfy the definition of "relatively inertial," but this seems wrong. Indeed, none of the subsequent formulas (like the law of addition of velocities) are satisfied for this example.

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