Re: [Phys-L] ? FCI --> momentum flow

[John Denker <jsd@av8n.com>]

On 11/01/2013 08:38 AM, LaMontagne, Bob wrote:

> Isn't the momentum of the top book upward?         [***]

1) In the lab frame, the book is at rest.  It has no momentum,
 upward or otherwise.

2) In any freely-falling inertial frame, there is no g-vector and
 hence no natural definition of "down".  However, in an attempt
 to capture the spirit of the question and not get unduly nit-picky,
 let's switch temporarily to the lab frame, paint big arrow on the
 wall labelled "This Way Down" and then switch back to the freely
 falling frame.  This arrow is somewhat unnatural and potentially
 misleading, so we will have to use it carfully, but for now I
 assume is the intended definition of "down".

3) Even then, we cannot say that the momentum of the book is
 upward.  The momentum is changing according to

         (d/dt) p = F                 [1]

 where F is the force exerted by the supports.  This force is
 in the "upward" direction.  However we cannot conclude that
 the momentum is upward.  We can find the momentum by integrating
 the equation of motion [1], but there will be a constant of
 integration.  Different freely-falling frames will have different
 constants of integration.  In some frames, the book will start
 out with an enormous momentum in the "downward" direction, which
 gradually over time becomes less downward.

> Due to the rigid nature of
> the earth and the books further down in the stack, the top book is
> being pushed radially outward relative to the surrounding flow of
> space-time.

That's all true in the freely-falling frame.

>  Where is the downward force?

We agree that the freely-falling frame, the only relevant /force/ is
"upward", using the somewhat-unnatural definition of "upward".

Note that upward force is not the same as upward momentum.  I mention
this because the top-line topic sentence [***] asked about momentum,
where as the last sentence asked about force.  There is a constant 
of integration.  Different freely-falling frames will have different 
constants of integration.