# Apparent Discrepancy Between Two Definitions of Newton's First Law

1. Apr 16, 2012

### Wormaldson

So I was reading through my textbook (specifically, Physics for Scientists and Engineers, Eighth Edition, Volume 1 by Raymond A. Serway and John W. Jewett Jr.) and I noticed that, in one of the "Pitfall Prevention" sections (which are usually quite helpful - not this time, evidently), it says "Newton's first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of external forces."

The example given to illustrate Newton's first law was a hockey puck floating on an air hockey table. This confused me, as isn't the hockey puck in static equilibrium in the vertical direction because the force exerted upon it by the air streams from the table "cancels" with the force due to gravity?

Seeking clarity, I looked to almighty Wikipedia for guidance, and was puzzled further when it stated that Newton's first law is applicable in the case where the object in question has zero net force acting upon it ("This law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant.")

Naturally I found this puzzling. Then, I though, "well, perhaps the textbook means to say that Newton's first law is only applicable in the absence of external forces in a certain direction. This made sense in the context of the hockey puck example - obviously, there wouldn't be any reason to discuss the vertical motion of an object that is assumed to only be moving horizontally, right?" But then that lead to another issue: wouldn't that mean that the statement from the Wikipedia article is wrong? Or, at least, an insufficient explanation? And shouldn't this kind of thing be clarified in the textbook anyway? So I'm a bit confused here. Any help would be much appreciated.

P.S. As a not-so-serious aside, isn't the term "textbook" a bit redundant? I mean, what else would one be expecting to find in a university-level physics book? :tongue:

2. Apr 16, 2012

### harrylin

I agree with you that it's a bad example, just as you say. Here's how Newton stated it:

Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

PROJECTILES persevere in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are perpetually drawn aside from rectilinear motions, does not cease its rotation, otherwise than as it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in more free spaces, preserve their motions both progressive and circular for a much longer time.

- http://gravitee.tripod.com/axioms.htm (simply press "cancel")
Well, Newton might have implied it, but it's a bit ambiguous - see definition IV, http://gravitee.tripod.com/definitions.htm
As we see, Wikipedia currently lacks any reference to its claim that "impressed force" means "net force". It would be nice (and required for Wikipedia) to have!

3. Apr 16, 2012

### Wormaldson

Thanks for the reply. Based on what you've said, I gather that I should: assume that the example from the textbook was indeed implicitly making the assumption that we should only consider forces acting on the hockey puck horizontally, and assume that the Wikipedia article should not be considered as a valid source of information on the first law due to the definition of an "impressed force" being more along the lines of "any individual force on an object" rather than "the sum of all forces on an object."

Is that correct?

4. Apr 16, 2012

### D H

Staff Emeritus
That's pretty bad, IMO. In my old Halliday and Resnick they say exactly the opposite, "Notice, too, that by implication there is no distinction in the first law between the absence of all forces and the presence of forces whose resultant is zero. ... Hence another way of stating the first law is: If no net force acts on a body its acceleration is zero."

5. Apr 16, 2012

### D H

Staff Emeritus
One thing that many of these introductory physics texts don't go on about in enough detail is that forces is subject to the superposition principle: Forces are additive. This is essentially Newton's Corollary 1 to his three laws, but to me his derivation implicitly assumes the superposition principle to prove the superposition principle.

6. Apr 16, 2012

### K^2

Looks like an error in the book.

There are some caveats about first law and inertial systems, but it doesn't sound like this discrepancy has anything to do with it.

7. Apr 16, 2012

### harrylin

Not exactly: as I found the definition ambiguous on this point I left the final answer open, waiting for more input. And while Wikipedia is unreliable, textbooks can also be unreliable and I now come to a different conclusion:
Ah right, the first Corollary, and even more the introduction to the second one ("composition and resolution are abundantly confirmed from mechanics") make clear that we should understand his definition of "impressed force" as the action by superposition - and indeed, by zero net force the accelerating action is also zero.

Last edited: Apr 16, 2012
8. Apr 16, 2012

### Steely Dan

To me it kind of sounds like the opposite. It is usually hopeless to be able to say that the net force on an object is ever truly zero in Newtonian physics because of the variety of forces that are acting on any object on Earth. Therefore it makes more sense to assume that Newton was just talking about what would happen to one object in an isolated system if you were to exert a force on it, and leave as a corollary the idea that if you have two forces acting in opposite senses, then the resultant acceleration vanishes.

9. Apr 17, 2012

### haruspex

The only valid interpretation I can put on what the textbook states is that they are merely pointing out that Newton's exact wording only says what happens in the total absence of forces. As far as I can see (and I checked the Latin some) he made no reference to net forces or sum of forces or cancellation. The insertion of the word "net" seems to be a later (and much needed) interpretation.

10. Apr 17, 2012

### harrylin

Funny, but that also sounds good to me.

11. Apr 17, 2012

### harrylin

The point to be clear about is his definition of "impressed force"; and as I said, I find that definition somewhat ambiguous concerning the topic here. How do you interpret that definition?

12. Apr 18, 2012

### Wormaldson

Thanks everyone for the replies, unfortunately I'm still unsure as to how exactly the First Law is supposed to be interpreted. Is there no universal general consensus on the matter?

And to supplement the information given I think I should include the entire quote from the textbook (I didn't think the second half of it was really relevant at the time, and perhaps it still isn't, but hopefully it may shed some insight as to at least why it was written as it was: "Newton's first law does not say what happens for an object with zero net force, that is, multiple forces that cancel; it says what happens in the absence of external forces. This subtle but important difference allows us to define force as that which causes a change in the motion. The description of an object under the effect of forces that balance is covered by Newton's second law."

That seems more than a little at-odds with the information that has been given in the thread thus far.

13. Apr 18, 2012

### harrylin

It's I think consistent with the view expressed here by Steely Dan.
And it also seems to fit with Newton's definitions.