[Phys-L] momentum ... as used in the laws of motion

[John Denker <jsd@av8n.com>]

On 08/18/2016 07:55 PM, Anthony Lapinski wrote:

> I would not equate the first law with conservation of momentum.

The /third/ law expresses conservation of momentum.

On 08/19/2016 05:40 AM, Richard Tarara wrote:
> I think that all of Newton's Laws can be expressed in terms of
> momentum.  

Yes.

> Isn't that essentially what Newton did?

Well, yes and no.  The second law was formulated in terms of momentum.
However, the third law was originally formulated in terms of "action"
and "reaction", which is not ideal.  For details, see below.

> While we separate
> them into three distinct 'laws' it seems to me that they are all
> aspects of the same basic physical phenomena.

Here's my take on all that, in non-numerical order:

3) The third law expresses conservation of momentum.  Newton did
 not express it this way, but we are free to reformulate it based
 on modern understanding.

 As usual, there are lots of possible ways to arrange the pedagogical
 sequencing.  One viable possibility is to start (on Day One of the
 course with) the idea of conservation, and proceed from there.  So
 the third law comes before the second law.  Some recent "research-
 based" textbooks do this.

1) From our point of view as professional physicists, the first law
 is just an obvious corollary of the second law, in the case where
 the force happens to be zero.

 However, the first law exists as such for pedagogical reasons.
 It notifies everybody that we are discarding a ton of historical,
 philosophical, and metaphysical baggage.

2) The second law can be expressed in terms of momentum, and in fact
 that's how Newton did it.  He didn't call it literally "momentum",
 but there is no doubt that this is what he was talking about.

Note: The second law is not a corollary of the third, nor vice versa.
There are two separate nontrivial ideas here.  In particular, the
second law connects force to momentum, whereas the third law does
not.  The second law applies at a point, whereas the third law
concerns the transfer of momentum from one region to another.

Note:  Sometimes people try to use the first law to /define/ what
we mean by straight line.  IMHO this is a mistake.  It leads to
circular arguments, quite needlessly.  I recommend defining "straight"
in terms of geometry (as opposed to dynamics).  See e.g.
  https://www.av8n.com/physics/geodesics.htm#sec-straight