reply to Rick

["Rauber, Joel Phys" <RAUBERJ@mg.sdstate.edu>]

> A quick question to JR:  In your non-inertial frame of the turning car,
> HOW do you 'maintain' Newton's laws through the use of your 'kinematical'
> centrifugal force? You have no agent for that force and although the
> 'force' can be said to act on you, on what do you act to maintain the
> third law.

An excellent question, and written in a way that is understandable and gets 
to the point.

This will be my first quick reply, I may wish to amend what I say in a 
future post; after I've had a chance to think carefully on the question. 
(Actually in retrospect it isn't a short reply, just quick)

solution (a):
I mentioned in a very recent post (which may not have been read by others) 
that I took a very utilitarian (operational) viewpoint toward Newton's laws, 
which will probably be quite evident in my reply. Hence this solution:
No one ever said you needed to use the 3rd law in order to solve problems 
with the 2nd law, you don't use it when dealing with external forces. (I'm 
not denying that it may useful at times in solving your problems, nor do I 
deny that a lot of problems are more easily solved and understood in 
inertial frames, but others aren't). As a practical matter, one only uses 
the 3rd law to deal with internal forces in a physical system you analyze 
(I'm going to have to learn how to spell that word!!). For example, the book 
resting on the table table top: there is a normal force of the table pushing 
up on the book and there is the 3rd law partner (the equal and opposite 
force), namely the normal force of the book pushing down on the table top. 
This invocation of the 3rd law relies on the agents causing  the forces to 
both be included in the system being analyzed. The kinematical forces, 
centrifugal for example, are external forces to the system being analyzed.

I think that even in problems analyzed in inertial frames, one never uses 
the third law to calculate external forces.  The moment you do apply it to 
that agent, you've implicitly included it in your system and now switched 
over to viewing it as an internal force.

So view them as external forces and the loss of the 3rd law for them is of 
no great loss. Incidently, even in inertial frames if I work a problem on 
the motion of two charged particles I'll be dealing with forces that don't 
obey the third law (this is a whole other nest of worms, saying this is a 
special relativistic in effect begs the issue unless one wants to imply that 
special relativity ruins the 3rd law). So again I don't find the loss of 
applicability of the 3rd law to be of great concern; I'm already used to 
dealing with forces like that inertial frames (by the way this difficulty 
for action at a distance forces, with finite propagation time, goes a long 
way towards showing the reality of fields, if you want to maintain 
conservation of momentum, the field is required as a carrier of momentum).

So I'd say as a matter of practice, the concern doesn't come up; we will 
simply treat them in the same manner that we treat external forces and 
merrily calculate away using the 2nd law and find we get correct predictions 
for all quantities in the equation, or combination of quantities, when 
compared against experiment as measured in the non-inertial frame(in so far 
as GR effects may be ignored). I've never said that there isn't something 
different about them; that's why I use the special adjective "kinematic", 
perhaps "effective" would be preferred or even "fictitous"; I just think 
that the word "kinematic" says exactly what they are and might therefore be 
the best adjective.

solution (b):
I don't like this solution! (but it is simply a matter of taste)and there is 
nothing inconsistent about it.

Simply posit a virtual agent that is responsible for the force and say the 
3rd law does apply. Nothing will change in our solution to the equations of 
motion (the 2nd law) and we will get all the correct answers, since we end 
up solving the same equations.


BTW I too find it most useful to usually work in inertial frames for 
problems; all I say is that you don't have to

Joel Rauber
rauberj@mg.sdstate.edu