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Why don't we just agree as follows:
a) Sometimes ma is calculated from F and sometimes vice versa;
b) The equation F=ma covers both cases.
Absolutely. I've never had a problem with that.
I can imagine a particle having its net acceleration resolved into a 3D
coordinate system. I personally wouldn't say that a(x), a(y), and a(z)
are three simultaneous accelerations; rather, I would say they are
components of the one acceleration. Then, when a(net) is zero, I would
say all the components are zero.
Where I have difficulty is imagining three simultaneous nonzero
accelerations that add to zero. The only observable result is a(net)
equals zero. I cannot oberve the individual nonzero accelerations. I
don't think it is a failure of my imagination or my experimental skill
that I can't figure out a way to measure them, I think they cannot be
measured in principle.