- #26

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Yes, and it's crucial that you mention that all your vectors refer to an inertial reference frame. The logic is that in Newtonian (as well as in special relativistic) physics there exist inertial reference frames and by definition (!) in this frames a free body moves uniformly (i.e., with constant velocity). This is the content of Newton's Lex I.That's not quite correct. The logical equivalent of the first expression is

[itex]{\rm If}\quad \frac{{d\vec v}}{{dt}} \ne 0\quad {\rm then}\quad \sum {\vec F \ne 0}[/itex]

Then there's a definition of force in Newtonian physics which is the time derivative of momentum (which of course needs the introduction of mass beyond the kinematical quantities). This is Newton's Lex II.