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Rolling/sliding ball



Hi Mark,
The "extra condition" is that of pure rolling, which can be
expressed physically as instantaneous zero speed of the
point of contact of the ball with the table or
mathematically as r times omega equals v. The process
depends on the surface being rough; if it is smooth the
initial conditions are preserved (on a horizontal table).
When pure rolling occurs the speed at the top of the ball is
twice the speed of the centre of mass and the speed at the
bottom of the ball is zero.
Brian McInnes
----------
From: Mark Lattery <lattery@VAXA.CIS.UWOSH.EDU>
To: PHYS-L@LISTS.NAU.EDU
Date: Fri, 30 Apr 1999 3:16 AM


Phys-l,

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

"Physical concepts are the free creations of the human mind and
are not, however it may seem, uniquely determined by the external
world."

--Einstein in "The Evolution of Physics" (1938)