# Question #65c36

May 2, 2017

Newton's three laws of motion are:

1. A body will remain at rest or move with a constant velocity unless acted upon by a force.
2. Force is equal to mass multiplied by acceleration.
3. To every action there is an equal and opposite reaction.

Suppose we have two prepositions as

1. If there is no force implies there is no acceleration
2. If there is no acceleration implies there is no change in velocity

The first one comes directly from Newton's second law stated above. The second one is definition of acceleration.

From these two we can conclude

If there is no force then there is no change in velocity

This is what Newton's first law states.
Hence this question!

Let us consider following example:

A person is seated in a compartment of a stationary train. As the train moves forward and leaves the station, the person experiences acceleration equal to the acceleration of the train. From the view point of the person it is the train station which is accelerating away.

Where is the force acting upon the station as required by Newton's second law of motion or proposition 1 above?

The fallacy of the statement that first law can be derived from the second law is due to not understanding how Newton defined force.

Newton stated that force is intimately connected with the co-ordinate system in which acceleration is measured. This definition leads to an important asymmetry: a force will cause an acceleration but an acceleration might not necessarily be caused by a force.
In other words

Only in a co-ordinate system, which is stationary or is moving with a constant velocity, will a body remain at rest or move with a constant velocity unless acted upon by a Newtonian force. In all other co-ordinate systems the body will accelerate even when no force is present.
Notice here that the italicized text is what Newton's First law of motion states.

Going back to proposition 1 above, we see that it pre-supposes the existence of first law.

Hence, the truth is that Newton's first law limits the scope of the second law and therefore it is an independent rule.

May 2, 2017

If you look at this translation you will see that the First Law addresses what we might now call Inertia. So, whilst in a way it may or may not be seen to fall within the ambit of the 2nd Law, the fact of inertia is a significant one, in and of itself. It certainly stumped the raving genius that was Aristotle. One might even argue (??) that it is the foundation upon which the 2nd law is built, much as the Zeroth Law of Thermo looks a bit obvious (mmm, maybe even silly) but is an important step in the definition of temperature.

So I'm not disagreeing with anything said here, or on the myriad other discussions that have occurred on the net on this topic. I just think the question may miss the point of the First Law. I don't know, that's just an opinion.

The other thing that may or may not be relevant here is that the first law was well known to yet another in this line of geniuses, Galileo. And it is almost inconceivable that he was unaware of the second law too. So in the classroom these are rolled out, much as Maxwell's are (Oliver Heaviside?!?!), as stuff he did, whereas his best stuff was way more remarkable and incredibly varied.

And, whilst on the subject, LOL, I'd like to give the Third law a big shout out. In particular, conservation of momentum is another remarkable fact of nature, but when you look at it through that very innocuous little 3rd law, conservation of momentum does begin to make great sense.

And FTR I think these discussions about the necessity for the 1st law are great, not because it matters but because it gets people talking in great detail about what the laws mean, as per the previous post. So, please, no noses out of joint :)

[Disclaimer: I have assumed that the translation is authentic. ]