Re: Apparent weight

[Leigh Palmer <palmer@sfu.ca>]

The Earth's surface is an accelerated frame. You must look at pucks
supported on an air table in a horizontal plane to see momentum being
conserved. That is because the momentum of objects free to fall near
Earth's surface is not conserved; they tend to gain momentum downward
due to the presence of an acceleration of the frame upward with
magnitude g. In a plane perpendicular to this acceleration, a
horizontal plane, momentum is conserved. In the space shuttle one
would not need to use an air table to demonstrate conservation of
momentum. One could collide tennis balls floating weightlessly in the
air just as well, easier to do, and with a lot less attendant noise!

"The" frame of reference of that rotating camera is very complicated.
At each point in its frame there will be an acceleration given by the
sum of the Earth's surface acceleration (the camera is attached to
Earth) and the centrifugal acceleration at that particular point.
Remember, one must always work locally. The relations work for only a
small region around the point of interest. The rotating camera frame
is not one frame; it is many different frames. "Horizontal" means
perpendicular to the local direction of the frame's acceleration, and
there are many different "horzontals" in the camera frames. In
addition to that, it is the case that the pucks will be moving in
horizontal planes in *none* of those rotating frames, so one will not
expect to find their momentum conserved anyway!

Leigh


> Leigh,
>
> Your first sentence from the paragraph below grabbed me.  Assume one has
> a 'frictionless' air table positioned on a lab table so the air table is
> horizontal or parallel to the surface of the earth.  If two pucks are pushed
> together and we photograph the
> interaction, momentum is conserved.  No problem thus far.  Now suppose we
> rotate the camera, positioned above the air table, at a constant speed.
> When we view the film, the pucks will appear to moved in curved paths due
> to the accelerating camera.  If I understand your first sentence,
> momentum will be conserved in the accelerated frame of reference.  I
> would have thought that momentum was not conserved.  Am I wrong or do I
> not fully understand what you mean by what I read below?  Would momentum
> be conserved for the colliding pucks in the accelerated frame of
> reference (due to the rotating camera) if I examined the movement of the
> pucks over a very short time period?  Thanks in advance for your answer
> and ideas.
>
> Lowell Herr
> The Catlin Gabel School
>
> > You will find that conservation of momentum is a principle that works
> > quite well in the horizontal plane in an accelerated frame. There is no
> > need to give it up. I'm very curious about how you teach your students
> > the first law of motion. I start by showing my students that we don't
> > live in an inertial frame. The first law is not trivial by any means;
> > it is a great intellectual feat to abstract to an environment one has
> > never experienced for any appreciable time - and lived to tell of it!