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Re: [Phys-l] pseudo-force



I would modify your description of modes 1 and 3 and sort of combine them. I would say the approach is to hold tight to Newton's 3 laws but when analyzing a non-inertial frame, do so by viewing it FROM an inertial frame (spinning carnival ride or orbiting space station as viewed by an observer in an inertial frame). One then recognizes that someone within the accelerating frame will feel and in fact measure forces that don't actually exist when viewed from the inertial frame--usually these are due to 1st law behavior. Then, to give some validity to these 'feelings/measurements' the term fictitious (pseudo) force is used.

This is my approach in intro classes (especially gen-ed). The utility here is to reconcile the Newtonian model with their own experiences within non-inertial frames. I would say it has a lot of utility (at least IMO). The classic 'Frames of Reference' film seems to have this approach although there they do concede that their fictitious forces are real to the person in the non-inertial frame.

Rick

----- Original Message ----- From: "David Bowman" <David_Bowman@georgetowncollege.edu>
To: "Forum for Physics Educators" <phys-l@carnot.physics.buffalo.edu>
Sent: Thursday, October 26, 2006 10:52 AM
Subject: Re: [Phys-l] pseudo-force


Regarding John Denker's questions:
Some questions:

What do people mean by the term "pseudo-force"?

I think they mean any tendency to cause an acceleration w.r.t. a
non-inertial reference frame that has no agent responsible for
producing it a la Newton's 3rd law and which is directly proportional
to an object experiencing it's mass, and which disappears in an
inertial refernce frame.


Is a pseudo-force a force?

I think that depends on one's definition of a force. There are at
least 2 ways of defining a force that are mutually incompatible and
where the incompatiblity is most accute in non-inertial reference
frames.


Why is it called a pseudo-force?

I think it is because those who hold to the first way of defining a
force by holding Newton's 3rd law more tightly than the other 2 laws
don't consider such a force to be an actual real force according to
their definition.

It is a fact that in classical nonrelativistic situations
(asymptotically slow speeds compared to c velocities, space-time
regions of gravitational potential low compared to c^2, and actions
macroscopically large compared to h-bar) Newton's laws only hold in
inertial reference frames. In non-inertial frames they contradict
each other. So in such a situation one naturally tries to salvage
some of their utility by extending them to such a situation by
defining things (e.g. forces) by holding to a subset of those laws
and letting the other ones that are violated be appropriately
modified for the non-inertial situation.

The first way to define a force is to hold on to N3 more dearly
than N1 & N2, and require that a force be an aspect of a mutual
interaction between different agents that exert mutually
equal and opposite forces on each other. In this scenario such
frame-dependent non-inertial tendencies to accelerate are called
pseudo forces or fictitious forces because they are not exerted
in pairs between interacting objects and thus do not satisfy their
definition of a force. In this scenario N1 and N2 are manifestly
violated in a noninertial frame. These laws can be formally made
to look satisfied by introducing those fictitious force to balance
the books, but everyone in this first school of thought knows that
this is just a dodge to hide the fact that N1 & N2 are violated in
non-inertial frames.

A second school of thought is to use N1 and N2 as defining the
meaning of a force. In this school of thought such frame-dependent
tendencies to accelerate are real forces and N3 is violated in that
there are now some forces that don't come in action-reaction pairs.
This violation can be hidden by proclaiming that the refernce frame
is the agency that generates these forces and that the objects
experiencing them exert reaction forces back on the refernce frame
but that the refernce frame itself by its very definition can't
accelerate w.r.t. itself, so it can be thought of as having an
infinite mass. But everyone holding to this 2nd school knows that
this is just a dodge to hide the violation of N3 and make things
formally look like all 3 of Newton's laws are holding.

A third school is to only consider Newton's laws as valid in the
first place in inertial frames, and to let them be violated in any
old way in noninertial frames, and to just restrict one's attention
to applying them in only inertial frames so that that their
violation in non-inertial frames never comes up in the first place.
I think this is a common strategy of many high school teachers.
They (probably rightly) complain that they have enough trouble
getting students to understand motion in inertial frames so that
adding in the further complication of analyses in non-inertial
frames is asking for a pedogogical nightmare.

My personal preference is to go with the 2nd school of thought but
not attempt to hide the violation of N3, but to rather just accept
the fact that some forces of nature don't come in action-reaction
pairs between identifiable bodies. My reasons for this choice are:

1) Only 1 of 3 laws of Newton are violated this way rather than 2
out of 3 being violated in non-inertial reference frames as is the
case with the 1st school.
2) Consistency and the Equivalence Principle require that those
holding to the first school admit that gravitational forces are
fictitious pseudo-forces. I don't want to admit this, so I like
the 2nd school.
3) We already know that N3 is violated anyway by magnetic forces
acting between electrically charged particles/current elements
moving nonrelativistically slowly.
4) It is at least cumbersome and probably problematic to consider N3
as applying to forces exerted by disembodied force fields.


Is this concept crucial/useful/marginal/unhelpful?

I guess I would come down somewhere near the boundary between
marginal & unhelpful.

David Bowman
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