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pool table physics



John Denker wrote:
I made a diagram that may help:
http://www.monmouth.com/~jsd/physics/pool.gif
You can calculate the horizontal component of the force. You can calculate
the torque. Plug in and turn the crank.
There's nothing wrong with the diagram, but the direction of the force
vector can't be chosen arbitrarily. It's determined
(up to a sign) by the standard model of kinetic friction.

I have been unable to identify a clearly-wrong assumption. I suspect there
are some unstated assumptions floating around.
Then it's not really necessary to discuss my description of the
collision as approximately symmetric. The model doesn't make an
assumption of symmetry; approximate symmetry was just my way of describing the
results of the model.

How sure are we that the system in question is actually optimal?
I discussed (www.lightandmatter.com/pool/pool.pdf) the relationship
between optimal rebound distance and rolling without slipping.
They're approximately equivalent. We observe the ball to roll
without slipping on the rebound (or at least, any deviations
from rolling without slipping are too subtle to see with the naked
eye).

I renew my recommendation that we speak of
-- sliding friction,
-- rolling friction, and
-- static friction (for strictly static objects only).
Maybe I'm misunderstanding you, but the only difference I can
detect between the way I define the terminology and the way
you define it is that you don't want to call it static friction
unless both objects are in an absolute state of rest. Such
a distinction would be unphysical, so maybe I'm not
understanding you.