# Clarification regarding Newon's first law.

1. Jul 29, 2012

### sankalpmittal

Hello ,
I am in class XI now and I am 15.

Ok , so I have a doubt :

Majority (no all !!) of our textbooks state Newton's first law as follows :

"Every object remains in its original state of rest or uniform motion unless it is acted upon by a net external force."

But our teacher told us that the definition in each and every book (nearly) is incomplete.

He told us that correct definition will be to say :

"If observation is being made from an inertial or non accelerating frame of reference , then every object remains in its original state of rest or uniform motion unless it is acted upon by a net external force."

He then gave us the following examples :

Suppose a block is kept at rest on a floor. An observer observes this standing beside the block and thus concludes that the block is at rest. So |a| =0
Or |F| =0. So he says that Newton's first law holds.

Another observer in a car is moving with a velocity towards the block and observes the acceleration in the block as a.
So F = ma
So he says that the newton's first law is wrong , as there is an external force being applied and object was at rest!

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Now here are my views regarding this :

I think that the teacher is confusing relative acceleration or relative force with frame of references.
For example another observer in a car is moving towards the block with velocity v.
The velocity of block with respect to car is given by :

vb/c = -v

If we differentiate this , we get :
dvb/c/dt = -dv/dt

"ab/c = -a"

Also relative momentum of block w.r.t car is :

pb/c = -p

If we again differentiate this , we get :

Fb/c = -F

Thus the above expression gives force on block w.r.t car.

Also , I think that inertial frame means that newton's first law isn't applicable inside the frame.

I think that every textbook just can't be incorrect.

2. Jul 29, 2012

### Staff: Mentor

Apparently that car was accelerating. Viewed from an accelerating frame, Newton's first two laws require modification.

3. Jul 29, 2012

### TobyC

Newton's 1st law is actually more of a definition of which frames are not accelerating. It's true that Newton's laws have to be modified when you move into an accelerating reference frame, but what is an accelerating reference frame? Accelerating with respect to what? The best way that I've heard Newton's 1st law stated is "There exist frames of reference in which particles move at constant velocity when not acted on by external forces". Once you have established the existence of these frames, it is clear that all these frames must be moving at constant speed with respect to each other, so you can define this set of frames to be the non-accelerating frames and measure acceleration with respect to them.

I think that definition is superior to what you've quoted as the textbook definition, which is oversimplified because it doesn't acknowledge the fact that Newton's laws only apply to specific frames of reference. I think it is also superior to your teacher's quoted definition, because actually you can't really define absolute acceleration without using something like Newton's law as a reference point. Your teacher's definition appears to have it sort of backwards.

4. Jul 29, 2012

### krd

The way the law is written in every text book assumes that the frame of reference the object is in is the entire universe.

Your teacher has it half baked.

The law states simply, objects do not change their course or velocity unless an external force acts on them.

He's wrong for other reasons. When you drop an apple, does it experience the force of its' mass by acceleration, or the mass of the earth by the apple's acceleration. Do you feel the force of the moon's velocity.

With Newton's first law you're better off just to forget about acceleration - acceleration requires external force. Take an accelerating car, the extra fuel burned to accelerate the car is considered an external force for the purpose of the law.

5. Jul 29, 2012

### krd

But then it's not Newton's first law.

You can't give an object energy just by observing it.

Damn I just thought of another problem for high speed space travel.

If you're in a space ship. travelling towards a galaxy, at near the speed of light - the normally pale photons from the galaxy, will be highly energised and melt you and your spaceship. Your velocity will Doppler shift them to a much higher energy. Not all that relevant but just thought of it.

6. Jul 29, 2012

### TobyC

Wrong isn't the word I would use, strictly speaking it's actually right, I just think it's badly phrased because it's better to use Newton's 1st law to define which frames are accelerating, not using the concept of acceleration to define Newton's 1st law.

The textbooks assume an inertial frame of reference when they state their definition (I don't know what you mean by 'the entire universe') and that's why the textbooks aren't wrong either, they're just simplified so as not to confuse students starting out in physics.

Exactly, Newton's 1st law only applies in special reference frames. If you start from scratch looking at the mess of particles moving through space and time that is the universe, there's no way you can initially decide which coordinates you should be using. There's nothing to use as a reference point to define absolute acceleration for instance. It turns out that there are special systems of coordinates in which the laws of physics take nice simple forms. You call these inertial systems, and in these systems only, Newton's laws including his first apply. In other systems the laws of physics describing how particles move would look very different. This gives you a way to define absolute acceleration, because you say inertial frames are not accelerating and you measure all other acceleration with respect to them. If you're in an accelerating car you can tell, and measure your absolute acceleration, by the fact that objects left on their own will accelerate backwards, not what you'd expect if Newton's first law applied.

7. Jul 29, 2012

Of course this is only true in an inertial reference frame.

8. Jul 29, 2012

### D H

Staff Emeritus
The teacher was correct. The modern interpretation of Newton's first law is that it defines the inertial frames of reference. There is nothing in Newton's writing about a universal frame of reference; there's nothing in Newton's writing about frames of reference, period.

9. Jul 29, 2012

### krd

The whole idea of the law is it's a simplified starting principle. There isn't anything in the universe that doesn't have an external force acting on it.

When you start dragging reference frames into it, you're muddying the water.

10. Jul 29, 2012

### sankalpmittal

Ok , but that's not what I asked for. However thanks for clarifying this

Ok I get the idea regarding this. My guess is that every textbook states the definition of newton's first law on "Earth". As we "practically" regard "Earth" as an inertial frame of reference , Newton's first law will hold true there. So the textbook's definition is simplified though. Am I correct ?

So teacher's definition is correct then.. However I am not at all convinced by the examples he gave :

So suppose we take the block kept on ground as reference frame ,S. Since earth is practically an inertial frame , so frame S will also be an inertial frame. Also let the observer standing beside block be taken as frame S'. Since frame S' is at rest with respect to frame S , so frame S' will also be an inertial frame. Now another observer in car moving towards the frame S be taken as frame S''. Since frame S'' is accelerated with respect to frame S , so frame S'' is a non inertial frame. Now inside frame S'' newton's first law just can't be applied.
How does he dragged concept of frames here.

Again he is confusing frame of references with relative force. Like I stated :

Am I correct ?

So the mentors posts are stating that teacher's definition is correct , complying with TobyC and Dead Boss , however contrary to krd.

11. Jul 29, 2012

### D H

Staff Emeritus
Dragging reference frames into it is exactly what Newton's first law does. It is essentially a statement about frames of reference. Toby C put it very nicely in post #3 with his statement "There exist frames of reference in which particles move at constant velocity when not acted on by external forces."

12. Jul 29, 2012

### arildno

ACTUALLY, it is deep thinking about reference frames that clarifies the waters..

13. Jul 29, 2012

### Staff: Mentor

Sure you can. Or more specifically, energy depends on the reference frame. It is frame variant, not an intrinsic property of the object itself.

14. Jul 29, 2012

### krd

I don't know what Newton's original wording was, the law implies a frame of reference. And I don't think you need to explicitly state that the velocity can appear different in different frames of reference. I'm certain Newton was well aware of that too.

Other reference frames, in the instance of the law, are not relevant. They only become relevant when they need to be explicitly considered.

15. Jul 29, 2012

### Staff: Mentor

16. Jul 29, 2012

### krd

I'm too tired for this kind of argument.

By referring to external force in the original wording of the law, the frame of reference is implied.

17. Jul 29, 2012

### krd

I knew it was in Latin.

Have you read Principia in the original?

18. Jul 29, 2012

### Staff: Mentor

That is not correct. Any real force exists in all reference frames, and it even has the same magnitude in all reference frames. There is nothing about a real force which identifies a specific reference frame.

19. Jul 29, 2012

### D H

Staff Emeritus

However, this thread isn't about how Newton expressed his laws, or what he thought of them. It's about the modern interpretation of Newton's laws. Newton's original formulation is a bit irrelevant. The sciences don't place near the emphasis on the wisdom of the great minds as do the humanities. The original formulations of most scientific works are oftentimes clumsy, verbose, and not quite scientific. Newton's physics is a prime example. Newton didn't use calculus much at all in his Principia; Newton preferred not to do so if at all possible. Newton rarely used the concept of energy; Newton didn't think energy was conserved. He didn't use vectors; the vectors we use so freely nowadays weren't invented until 200 years later. He didn't use the concept of a frame of reference; that too was something invented long after Newton's death.

Most importantly, Newton's concept of absolute space and absolute time are not scientific. This absolute space and time are not observable by means of any scientific experiment. The same applies to your concept of a reference frame based on the universe. The concept of an inertial system as one in which Newton's first law of motion is valid was introduced a couple of hundred years after Newton.

This concept is falsifiable, and it turns out, is false. It took a couple of hundred years to fully formalized Newtonian mechanics through Hamilton's principle, make it nice and compact through the use of vectors, and made scientific in Lange's reinterpretation of Newton's first law. Just when this work of two centuries was finished, it was shown to be false by relativity and quantum mechanics.

20. Jul 29, 2012

### arildno

I'd like to add to DH's excellent post:

The wisdom of the ancients is honoured in science as well, namely in recognizing who made giant efforts of clearing away intellectual rubble of THEIR OWN TIME, finding a constructive path for future generations to walk along.
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Therefore, many of the great thinkers within science are easily misunderstood, because we have forgotten what they struggled AGAINST.

To take Newton's first law:
Essentially, it is a radical break with theories like the "impetus theory", and similar conception, namely that in order for objects to move at all, one thought there had to be some kind of self-propelling force WITHIN the object.

Not only do these theories conflate mechanisms for maintenance of velocity (the self-propelling force) with acceleration generators, but the theory also blocks the mentality for the true gem contained in Newton's 3.law:
IF one accepts a self-propelling force, then the whole idea of forces always acting IN COUPLES is very hard to come by, even sounding utterly false (the self-propellator is a counter-example, violating Newton's 3. law).
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Of course, none of this is really necessary to know about in order to learn and master physics, but nonetheless of some interest.