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I'm interested in how folks introduce Newton's first law (N1) to...
their classes.
A typical textbook says something to the effect that "N1 gives us a
criterion for determining if a reference frame is inertial"
(paraphrasing from Tipler). I have several problems with that:
(1) I like to distinguish "laws" (things about the world that do not
follow from mathematical deduction using definitions) and
"definitions" (useful but ultimately arbitrary decisions physicists
make). The above phrasing seems to reduce, maybe not to a logical
definition of "inertial frame" itself, but certainly at least to an
operational one.
Even as an operational definition, it puzzles me. Suppose I plunk
you down in some cubicle attached to some reference frame. ... Your
assignment, should you choose to accept it, is to
*experimentally* determine if your reference frame is inertial using
NI alone.
how do you know you've measured every last force on it?