Re: [Phys-L] sharing an activity re circular motion free-body diagrams

[John Denker <jsd@av8n.com>]

On 12/10/2013 06:53 AM, Paul Lulai wrote:
> Big F, 3 subscripts. One for the category (N, G, f, e, T) then one
> for the 'dealer' and one for the 'feeler.' In addition to reducing
> fictional forces (the force on the object because it is moving
> etc...) it also helps with N3L pairs.

Yeah.  That has a lot of advantages.

I like to write it as

          F_feeler<dealer>                  [1]

with the dealer in <...> brackets.

This is /sometimes/ unduly verbose, but in such cases it is easy
to use shorthand, e.g. by dropping unnecessary details.  Still,
form [1] should be considered the gold standard, and anything
else is at your own risk.

Among other things, this allows us to write F_i<j> as a square
matrix.  The third law requires this to be an /antisymmetric/
matrix.

The total force on object i is given by the sum over all columns
in the ith row:

          F_i = ∑_j  F_i<j>

There is not any corresponding expression for the sum over rows in a 
given column, not in common use anyway.  For 350 years the tradition 
in physics has been to focus on the total force /acting on/ the 
object, i.e. /felt by/ the object ... not the total force "dealt by" 
the object.

This is why in my notation the <dealer> is in brackets while the
feeler is not.  Also it is no accident that the pointy brackets
point away from the <dealer>.

Also:  It was mentioned that "double counting" was a problem that
must be avoided.  Well, sometimes that's true, but OTOH sometimes
double counting is exactly what you want.  In the aforementioned
matrix, every physical force appears exactly twice, once as F_i<j>
and once as -F_j<i>.  That is a Good Thing, so long as you keep
track of what you are doing.

Also:  As always, anything having to do with the three laws of
motion can profitably be translated from force-language to
momentum-language.
  http://www.av8n.com/physics/force-intro.htm

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

Once upon a time I saw a sign for a place called
	Emilio's Restaurant and Pizza

Now I would be OK with Emilio's Pizza, and I would be OK with
Emilio's Restaurant, but it can't be both.  It just can't.  It
might even be Emilio's Pizza Restaurant, but not "Restaurant
and Pizza".  As emphasized in Strunk and White, the elements
of a list should be parallel as to form and meaning.

I mention this because:

> 3 subscripts. One for the category (N, G, f, e, T) .......

Note the contrast:

 -- It is OK to categorize things by the nature of the force,
  such as gravitational or electromagnetic or whatever.
 -- It is OK to decompose the force into components:  radial
  component, tangential component, vertical component, horizontal
  component, and/or whatever.  This is tantamount to a choice of
  basis.
 
These are not the same thing.  These are two different lists.
You can have a tangential component of the electric field
along with a radial component of the gravitational field, or
vice versa, or whatever.