Is there a clever name for Newton's 2nd Law?

[Grasshopper]

Summary:: We all know of the "law of inertia" nickname for Newton's 1st law, but is there a clever name for the 2nd as well? What about the 3rd?

This may be the most inane question ever asked here, but I've spent some time searching and cannot find an answer. So many laws in physics and other disciplines have clever names: the law of conservation of energy, the law of diminishing returns, the law of conservation of charge, the principle of least action, etc...

But what of Newton's 2nd law? Surely someone has come up with a clever name...

 

[A.T.]

We all know of the "law of inertia" nickname for Newton's 1st law, ...

Never heard or used it.

 

[Grasshopper]

Never heard or used it.

Really? That's interesting. That's how I was first introduced to it.

https://www.britannica.com/science/law-of-inertia

However, that you have never heard the alternate name does actually kind of soothe my neurosis on this issue.

 

[gmax137]

Fudd's first law of opposition?

 

[mcastillo356]

First, Second and Third laws of Newton. Isn't easier?

 

[mpresic3]

The textbook Matter Interactions Modern Mechanics by Chabay / Sherwood, refers to Newton's Second Law as the momentum principle. I have seen the first law referred to as the Law of Inertia.

To be honest, I don't like it. The 3 laws of Newton are so well entrenched that learning other terms for them now will be confusing when you speak or write to other students, colleagues, etc. You are better off learning them and their order and meaning, that to try to get others to accept new names for them.

It is a good question though. Names do matter, when you are trying to learn something and may expedite the process. For example in the preface to the textbook (I think it is Fraleigh, Algebra, and I will look it up if anyone is further interested) the author says he tries to label his theorems in a way that is pedagogical. He refers to his cardplaying group and a game they play as "little red" where the lowest red card is wild. He states correctly that renaming in card game as "frustration" or "aggravation" would not be as useful in remembering the rule.

Newton's laws are the exception, however, and I think trying to call them something else with the physics community educated over the last century is just inviting confusion.

 

[sysprog]

Sometimes Newton's second law of motion is called the 'Law of Acceleration' $-$ the following is a not-especially-pithy English-language expansion of Newton's $F=ma$ equation: force equals mass [regarded as resistance to acceleration] times acceleration [acceleration being the second derivative of position with respect to time, given velocity as the first].

 

[mcastillo356]

And third, law of action-reaction

 

[jbriggs444]

Second law: "Definition of force"

 

[wrobel]

Second law: "Definition of force"

such a phrase needs a long explanation not to be looked as a banal mistake

 

[mcastillo356]

What Newton first stated in his 2nd law was about linear moments. It can be, as jbriggs say, the definition of Force: $\dfrac{d\vec{p}}{dt}=\dfrac{d(m\vec{v})}{dt}=m\dfrac{d\vec{v}}{dt}=m\vec{a}$

 

[wrobel]

For example in Arnold's "Math methods of classical mechanics" we read

then how can a function of $x,\dot x,t$ be identically equal to $m\ddot x$ as it jbriggs444 claims?
That is way I say that questions like "what is force by definition?" need accuracy.

 

[mcastillo356]

https://physics.stackexchange.com/q...rinciple-of-determinacy-intuitive-explanation
This might be redundant for you: does it help?
Greetings!

 

[jbriggs444]

then how can a function of $x,\dot x,t$ be identically equal to $m\ddot x$

You missed the part where you defined what force is. If you do not define it otherwise then a definition in terms of mass and the second derivative of position is as good as any other.

 

[wrobel]

I prefer to think that we choose the function $F(t,x,\dot x)$ such that the solution of the differential equation $m\ddot x=F(t,x,\dot x)$ would have been consistent with the result of experiment. If $ma$ is a definition of the force then the 2nd Newton law is just a tautology and gives nothing.

 

[Scott Mayers]

The second law is actually a 'definition' in light of the first law of inertia. All the laws are more appropriately "postulates" of Mechanics and normally a definition is separated from postulates in logic.

If "kinematics" is the stage of labeling without concern to time, then this might also be thought of as the first "Dynamic" law (?). I don't like the logic that separates these though and so perhaps it is just as appropriate to be under 'Kinematics'. I don't like the term, "kinematics" given it is rarely used and may get confused with other areas. Basically, it describes a link of the theory to logic (via the 'math' used in expressing it.)

It might also be considered the defining of the symbolic relationships in math as it relates to physical reality WITHOUT actual meaning until the theory is demonstrated to give it meaning. In this way, some logics treat this as undefined terms. This throws some off but if you have ever programmed, it might be like the initial step of assigning variables without interpreting its contents that RESERVE the label to be defined specifically later on. Often in computing, this would be assigned at that stage the value of 'zero' but it doesn't require defining until later.

As a 'law', it might be considered similar to a rule in a game you are playing in which to be elible to play, all players must at least agree to the labels being used AND to postulate that the referents of the symbols are agreed to be about real observed measures.

Whether you use the 'momentum' definition originally set up by Newton or the more common modern 'force' definition is trivial. The law postulates a defining SPECIAL case of the first law/postulate in that it specifically describes the intuitive meaning of 'inertia' provided there. The law of inertia is itself a kind of extension of logic's first universal law of consistency as it applies to what we expect nature. ["Law of Identity" is the more popular term for that logical law and it is related to this in that we expect something to remain constant.] The only caveate is that it doesn't assert the same consistency beyond an inertial frame. That is, it doesn't assert consistency as a rule for accelerating bodies. This needed Einstein's General relativity to be more 'complete'.

So where the fist law is a postulate (based on intuition about consistent behavior) for velocity of a given mass, the second law is a postulate about changes with respect to other masses moving with the same law of inertia where they conflict with one another that breaks up the 'consistent' behavior of each independently.

Then the third law is a law of conservation of two (or more) conflicting objects after contact.

Think of this as a possible way also: The first law can be thought of as a law of 'consistency', the second of 'inconsistency' and the third as a kind of 'resolution' of what becomes 'inconsistent' to be understood as 're-consistent' when looking at the larger frame to maintain "conservation".

 

[Grasshopper]

Thanks everyone. I was given much more than I thought I would be given.