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According to https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion Newton's First Law of motion is

In an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.

My question is: Does Newton's First Law depend on the object having mass?

In the statement of the law mass is not mentioned. Also if it has mass, as its mass tends to zero it would seem that the law would hold for each value of mass no matter how close to zero. Then why would it not hold in the limit for zero mass?

Another statement of the law from http://www.physicsclassroom.com/class/newtlaws/Lesson-1/Newton-s-First-Law is:

An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Again mass is not mentioned. It seems to me that, theoretically, the law should hold for zero mass. {I am talking about a hypothetical zero mass object in a Newtonian framework--not a real world object} For the most part the term 'momentum' could be substituted for 'mass' here.

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    $\begingroup$ Newton's laws were not formulated with respect to a theory of mass to include objects with 0 mass. f=ma breaks down as you set m=0, because any force on a massless object will result in an undefined acceleration. $\endgroup$ Sep 1, 2017 at 17:51
  • $\begingroup$ But would a massless object set in motion stay in motion with the same speed and in the same direction unless acted upon by an unbalanced force? $\endgroup$
    – user45664
    Sep 1, 2017 at 17:56
  • $\begingroup$ Under Newtonian physics, that would be the conclusion, that however does not happen in the real universe. $\endgroup$ Sep 1, 2017 at 17:58
  • $\begingroup$ This is a hypothetical question--not real (Newtonian) universe. Also re. your f=ma, (or a=f/m), if f is made a function of m (say f(m)=2m) and then take the limit as m tends to zero, the acceleration will remain 2 even for m equal to zero. $\endgroup$
    – user45664
    Sep 1, 2017 at 18:07
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    $\begingroup$ A theoretical Newtonian universe would likely have no objects with 0 mass as all such objects would be unstable to the influence of any other object if you take Newton's first and second law as it is. $\endgroup$ Sep 1, 2017 at 18:25

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You should first understand what is the speciality of Newton's first law. You should know that the first law can be derived from the second law. Then why did Newton give the first law at all? The reason is that, first law defines the reference frames in which the second law can act. From the statement of the first law, it is clearly understood that Newton has spoken of inertial reference frames as the frames of reference in which his second law can act, though he didn't speak of reference frames directly, as there was no notion of reference frames in his time.

None of Newton's laws are applicable in case mass is 0. If mass itself is 0, then the concept of Inertia doesn't arise, as a result of which the frame no longer remains inertial. Moreover, $F=\dfrac {dp}{dt} $ itself doesn't hold for zero mass, as the acceleration becomes undefined. As a result, if the universal second law is itself not applicable, then there is no question of applicability of the other laws.

It may be noted here that $m$ may $ \rightarrow 0$ but can never be $=0$.

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  • $\begingroup$ I am referring to the limiting case where mass tends to zero. Previous eg.: for f=ma, (or a=f/m), if f is made a function of m (say f(m)=2m) and then take the limit as m tends to zero, the acceleration will remain 2 even for m equal to zero. I think the variables can be defined such that none blow up. $\endgroup$
    – user45664
    Sep 1, 2017 at 18:21
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    $\begingroup$ I mean how can first law be derived from second law? Its a $\textbf{LAW}$. Newton's law are empirical in nature. It cant be derived. Its purely based on observation. $\endgroup$
    – sbp
    Dec 29, 2017 at 17:47

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