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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I took it from Wikipedia : "All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating". You have missed the word "rectilinear"!!!
Yes, the Wikipedia def'n makes sense, even if it isn't very rigorous. Perhaps the MIT writers can correct the reading.