# Why do we need Newton's First law? And how the First law works?

1. Jun 27, 2014

This must have been asked before. But never mind here I ask it again to convince myself.

Newton's Second law says $\vec{F}$ = m$\vec{a}$
Now if we put $\vec{F}$ = 0 here we get $\vec{a}$ = 0 which is Newton's First law.
So why do we need to state First law as a separate law?

Before I asked this I did little bit of searching. And what I got is - First law is necessary to define the Inertial reference frame on which Second law can be applied.

But why can't we just use Newton's second law to define Inertial frame? We can say $\vec{F}$ = m$\vec{a}$ is the Second law. So if $\vec{F}$ = 0 but $\vec{a}$ $\neq$ 0 (or vice versa) then the frame is non inertial.

One can say (can one?), we cannot apply Second law to define Inertial reference frame because the Second law in valid only in Inertial frame. Thus unless we know in advance that a frame is Inertial, we cannot apply the Second law.
But then why this is not a problem for first law? We don't need to know in advance if a frame is inertial to apply first law because we take First law as definition of inertial frame. Similarly, if we take Second law as the definition of Inertial frame, it should not require to know if a frame is Inertial or not to apply Second law (to check if the frame is inertial).

So, what's the reason for First law to exist?

[EDITED]

Last edited: Jun 27, 2014
2. Jun 27, 2014

### A.T.

An "inertial frame" is a frame where any object without external forces either remains at rest or continues to move at a constant velocity.

3. Jun 27, 2014

### sophiecentaur

I think Newton's First Law is very relevant because of its historical context. Before he formalised it, people thought that things naturally slow down (as they do - but for a good reason) yet could not square this with what went on with astronomical objects. N1 is a statement that unifies what goes on down here and up there. Well worth writing, IMO.

4. Jun 27, 2014

Thanks but I know what an Inertial reference frame is. But why it's the First law which is credited for the definition of Inertial frame?

So Newton's first law exists as a separate law just for its historical context?

5. Jun 27, 2014

### olivermsun

Well, most basically because there are other frames in which the First law does not hold. That is, an object is observed to accelerate in the absence of any force defined in that frame.

Or you could say that it tells you the exact set of conditions under which the second law is claimed to be true.

6. Jun 27, 2014

### sophiecentaur

It will be a long time, if ever, before they stop teaching Newtonian Mechanics as a first step for students and I don't thing that the historical context should be neglected. When you get down to it, N1 is only a special case of N2 but it's still worth keeping 'if only' for the historical context.
It's easy to forget that the notion of a 'frame of reference' is quite a struggle for a beginner. Using an assumed Earth frame for your first mechanics experience is surely acceptable.

7. Jun 27, 2014

### UltrafastPED

Newton's First Law of Motion also provides a physical test; if there are no net forces, then one sees inertial motion. If one does not see inertial motion, then there must be unbalanced forces.

Newton's version is an improvement upon the work of Galileo - see "Two New Sciences" - and Descartes. But the first law is the "setup" for the application of Newton's Second Law of Motion.

Some modern presentations prefer to start with symmetry principles; when this is done the "laws of mechanics" are expressed in much different form. This is convenient when the subject is analytical mechanics, i.e., Lagrangian and Hamiltonian mechanics.

Newton's First Law of Motion also describes the motion in the _absence_ of net forces: it continues as before (in this inertial reference frame), moving in a straight line, with unchanged speed.

This is why it is called the Law of Inertia. The expression "F=ma" is consistent with this. Newton constructed geometric proofs from the laws and definitions provided; being one of the world's great mathematicians and geometers, he would not have introduced an axiom or law which he felt to be unnecessary.

Last edited: Jun 27, 2014
8. Jun 27, 2014

But can't the Second law provide the same thing?

9. Jun 27, 2014

### Staff: Mentor

This point about historical context is important. It is not at all unusual for the modern formulation and presentation of a theory to be very different (mathematically cleaner, more crisply formulated axioms, all neatly trimmed with Ockam's razor) than the stumbling path that that the pioneers followed. It's a lot easier to plot a direct path when you already know your destination. (Both quantum mechanics and special relativity also followed this pattern).

It is, and in the 17th century that setup was much more necessary than it is in the 21st century. In the 350 years in between, we've come to accept the second law to such an extent that it feels natural to start with it and watch the first law fall out of the $F=0$ case, rather than following Newton's path. Back then... not so much.

Although science and the history of science are deeply entwined (you cannot study the latter without understanding the former; and although you can use physics to solve problems without knowing the history, it is very difficult to make new contributions to physics without knowing the history) they are different disciplines.

Last edited: Jun 27, 2014
10. Jun 27, 2014

I see that historical context is really crucial here. But then just to be sure, can we say that Newtonian mechanics can be formulated by using just his Second and Third law? ...While the First law is a reminder of the intellectual leap that had to be taken at Newton's time.

Hmm... Still, a great mind like Newton obviously noticed that his first law is a special case of his second law. But he kept it as a separate law anyway.

Well, so the first law stays. :tongue2:

Thanks everyone.

Last edited: Jun 27, 2014
11. Jun 27, 2014

### D H

Staff Emeritus
You're looking at it wrong, Adjoint. Just because you get a constant velocity from the second law with zero net force does not mean the first law is a special case of the second. The first law stands by itself. The other two laws must necessarily be consistent with that first law (and they are). It is that need for consistency that makes the first law appear to be unnecessary.

The modern view is that the Newton's first law establishes the context in which Newton's other two laws are valid. A rotating observer can invent fictitious forces to make Newton's second law appear to be valid, but now there's a new problem: There are no equal but opposite forces on some other object to those fictitious forces.

12. Jun 27, 2014

Thanks DH.

In the example you gave - I see that the inconsistency appears because the reference frame in non-inertial. That was certainly your point, right?
But I am not completely clear how the First law (and only the first law) can rescue us from here?

As far as I understand, the first law would say, the particle here (in a rotating frame) is changing its velocity or accelerating without any force acting on it. So the reference frame in non-inertial.

But cant the second law say the same thing? The second law can say, well here a ≠ 0 but F = 0, so this is a non-inertial frame.

I don't understand why an observer would invent a fictitious force when he applies the second law but won't invent a fictitious force when he applies the first law?

Would you explain a bit more please?

13. Jun 27, 2014

### olivermsun

How would you determine that F = 0? Normally you would measure m and a and infer F, right? So if you're in a rotating frame and you measure a nonzero a for an object which is actually in inertial motion, then what? Is there an F acting on that body?

14. Jun 27, 2014

### sophiecentaur

Just imagine a humanoid society that had evolved on a massive wheel, set in motion by some previous, extinct civilisation. They develop 'a Mechanics'. Whilst it would get to the same stage as ours, eventually, would they have got there (or not) with their own version of N1, on the way?

15. Jun 27, 2014

### olivermsun

On a massive wheel, like... the rotating Earth?

16. Jun 27, 2014

### A.T.

The definition above is just a reformulation of the First law.

17. Jun 27, 2014

You are pulling me back to my first question. I understand that the first law gives the definition of Inertia. What I don't understand is why we can't say that the second law does the same?

18. Jun 27, 2014

### olivermsun

19. Jun 27, 2014