# Does Newton's First Law depend on the object having mass?

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.

• 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. – A. C. A. C. Sep 1 '17 at 17:51
• 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? – user45664 Sep 1 '17 at 17:56
• Under Newtonian physics, that would be the conclusion, that however does not happen in the real universe. – A. C. A. C. Sep 1 '17 at 17:58
• 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. – user45664 Sep 1 '17 at 18:07
• 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. – A. C. A. C. Sep 1 '17 at 18:25

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 $=0$.
• 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. – sbp Dec 29 '17 at 17:47