Re: God damnit Bambu... You too Bob!

In article
<42c3e622-3538-46f7-98be-50b8ea0d2605@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Jal <jal@xxxxxxxxxxxxxxx> wrote:

How sure are you that the tilt of N has nothing to do with the ball's
speed at some particular moment?

You can measure the effective table tilt by measuring the time it
takes the ball to roll to a stop. If the effective tilt were
different at different speeds, you would get different results for
short distances than for long distances.

Another way to measure this is with a video camera. You can stop
the frames every 1/30th of a second and view the distance. This
gives a trajectory, and the distance vs. time should trace out a
parabola if the cloth results in a constant tilt, and some other
curve shape if the tilt changes.

As far as the alignment of the spin axis, this is because the
acceleration during the sliding part of the path brings them into
alignment. I posted a detailed description of how this happens for
the cue ball after a cut shot a few weeks ago. It is analogous to
the way the horizontal rolling component of the spin always changes
toward the natural roll state. In the natural roll case, the ball
either speeds up or slows down to bring the ball to the natural roll
state. In the axis tilt case, the ball curves a little to the left
or right as necessary to bring the axis into the right plane. If
you know the axis tilt, then you know how much curve is required to
do this, and because the axis tilt is so small, it is only a
fraction of a millimeter over the sliding distance. After the
object ball is hit, the sliding distance might be a few inches or
few diamonds (depending on shot speed), so it is difficult to see.
However, for the case where a spinning ball rolls to a stop, that
distance is very small, so you have at least a chance to see it then.

$.02 -Ron Shepard
.

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