If I lightly tap a cue ball on a pool table, it eventually rolls to a stop.
If the ball is tapped above some critical point above the center-of-mass,
the ball speeds up a little first until friction brings the ball into a
state of pure rolling. My understanding is that as the peripheral speed
rises in time (immediately after the tap) the center-of-mass speed falls,
until the two merge, and then the two drop to zero or remian constant
together, depending on your assumptions about the table .
However, this behavior doesn't come out of the standard mathematical
formulation of the problem. What needs to be added to the standard
equations to get the observed "kink" in the peripherial speed-time graph?
Do we need to take into account the gross imperfections in the table? (I
could see how a ball rolling across a shaggy rug would slow down as the
bristles in the run bend back.) Could you lend insights?
ML
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Mark J. Lattery Phone: (920)424-7105
Assistant Professor of Physics Dept: (920)424-4433
Department of Physics and Astronomy Fax: (920)424-0894
University of Wisconsin Oshkosh Email: lattery@uwosh.edu
800 Algoma Boulevard
Oshkosh, Wisconsin 54901-8644
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