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Re: A problem: linear momentum, angular momentum, dissipation



At 07:01 AM 8/5/01 +0530, D.V.N.Sarma wrote:

It is true that the line of action of the normal reaction is displaced
towards the front edge

OK.

and the distance between the lines of action
of the weight and the normal reaction can be shown to be ka/2.

Where does this k come from?
It's highly non-obvious that the distance is ka/2.
It's not even true, unless you add a lot of implausible assumptions.

Now my question is this. For the specified axis in the problem the
torque due to the weight and the normal reaction is the ONLY
torque that can reduce the angular momentum.

OK.
But that's true only because of the choice of the axis (datum) used to
gauge angular momentum. There's no deep physics in it.

But neither weight
nor the normal reaction are among the traditionally dissipative
forces.

I suppose that's literally true, but what does it mean?
Why is it relevant? Why is it interesting?
The balance of forces doesn't recognize a distinction between dissipative
forces and nondissipative forces. Ditto for conservation of linear
momentum. Ditto for conservation of angular momentum.

No doubt, the separation of their lines of action contains 'k'
and the magnitude of the torque is kmga/2.

Au contraire, I doubt it very much.
The linear momentum and the angular momentum both start out nonzero and
both end up zero. But that's all you can say about it.

There is no reason to believe that either one of them decreases according
to any special law, and there is every reason to believe that they don't
decrease according to the same law.

Proof: Example: Replace the block by a car, a typical automobile. The
wheels are supported on springs and shock absorbers. If you suddenly apply
the brakes, the nose dips. It returns to its normal position _after_ the
linear motion has ceased. If the shock absorbers are defective, the car
will oscillate around the pitch axis a few times before settling down.

In the case of the block, it is unphysical to imagine that the block and
table are so perfect that the analogous complex pitching motion is
absent. It's just harder to see and harder to talk about. Assuming the
block is supported in some special magical way is almost (but not quite) as
unphysical as imagining magical non-dissipative couplings for railroad cars
as discussed a while back:
http://mailgate.nau.edu/cgi-bin/wa?A2=ind9911&L=phys-l&P=R37089

Can we say that a
dissipative torque can be due to nondissipative forces and a
dissipative separation?

Why would we want to say that? Would such an assertion be
surprising? Would a diametrically opposite assertion be surprising? I
have no idea what a "dissipative separation" is.

There is a law of conservation of momentum. This has implications for the
balance of forces. But remember that TOTAL momentum is what is
conserved. It would be quite wrong to think that "disspipative"
contributions to the momentum obey their own separate conservation law.

I am baffled by the question. It seems analogous to asking me to prove
that apples times oranges does not equal 17. If there is some deep content
to the question that I'm not appreciating, please explain.