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Re: [Phys-L] feeler-dealer, third law, et cetera



On 12/13/2013 12:04 AM, Bruce Sherwood wrote:
"If you believe that momentum is conserved, define force as dp/dt and --
shazzam! -- you've got a nice, general, robust version of the third law."

Really?

Yes. Really.

Didn't we just go through a lot of discussion about distinguishing
between a particular force and a sum of forces?

Yes, we did.

I can't just replace F/-F > with dp/dt's,

You could if you wanted to.

because dp/dt is equal to the NET force on an object. It
isn't equal to the F's in the historical Newton's 3rd law except in the
special case of there being just two objects that are interacting.

Not true.

You're a smart guy. You could figure it out. There is some
interesting and important physics here.

For starters, when I speak of conservation of momentum, I
mean /local/ conservation of momentum. Among experts, this
should go without saying, because special relativity demands
that anything that is conserved /must/ be locally conserved.
If you want the next level of detail, this is spelled out in
the book _The Character of Physical Law_ by some guy named
Feynman.

In particular, the un-numbered equation about 20% of the way
down page 118 in _Matter and Interactions_ is emphatically
labeled *CONSERVATION OF MOMENTUM* but alas it is not a
sufficiently local statement ... except perhaps in the special
case of just two object interacting. It is more a statement
of constancy than conservation. It is a corollary -- but only
a corollary -- of the fundamental principle.

So .... If you believe that momentum is /locally/ conserved,
define force as dp/dt and -- shazzam! -- you've got a nice,
general, robust version of the third law.

For more discussion on the relationship between force and
momentum, with diagrams, see
http://www.av8n.com/physics/force-intro.htm#sec-momentum-flow
The /local/ boundary flow issue is discussed at
http://www.av8n.com/physics/force-intro.htm#sec-flow-boundary

For more about /local/ conservation and its relationship to
the continuity of world-lines, see
http://www.av8n.com/physics/conservative-flow.htm

======================

Also, please let's not get hung up on the "historical" laws
of motion. The 17th century has been over for a while now.
Our understanding of physics has advanced since then. The
advances do not require us to rename the laws after me (as
some have suggested) or even to renumber the laws.

Among other things, let me point out that Newton did not
express the laws of motion -- or anything else -- in terms of
vectors. Not ever. This stands to reason, given that vectors
were not invented yet. The same goes even for Maxwell and
electromagnetism, many decades later. This does not prevent
us from writing the laws nowadays in vector form or even (!)
4-vector form. It does not require us to rename the laws.

On 12/12/2013 06:49 PM, Craig Wiegert wrote:

Oh, come now.

If your goal is to ensure Newton gets credit for his Holy Laws, then by
all means make sure students learn them by number. I know from
experience just how few of them understand which numbered law
corresponds to which physical principle. By contrast, my students who
learn the Matter and Interactions style of "kooky jargon" have no
trouble recognizing and applying the principle, and at the end of the
day can still attribute it to Saint Isaac.

Physician, heal thyself. If your students are attributing
the first law to Saint Isaac, they are doing so incorrectly.

Contrary to what it says on page 6 of your textbook, Newton did
not originate this law. It was clearly set forth by Galileo,
many decades before Newton came on the scene. Sir Isaac was
the first to set it atop a numbered list, but that does not
mean the idea should be attributed to him.

"Imagine any particle projected along a horizontal plane
without friction; then we know, from what has been more
fully explained in the preceding pages, that this particle
will move along this same plane with a motion which is
uniform and perpetual, provided the plane has no limits."
– Galileo Galilei (1638)
tr. Crew & Salvio