A bawl in a rotating dish (was Hot air rising ...)

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

Clever. But I do not see why should the surface be parabolic?
Do you want the meridional radii of curvature to increase
progressively as the ball is climbing higher and higher? Why
should this be important? In my opinion any smooth concave
dish, even a wooden salad bawl, would be sufficient. Is this
correct? And I am not sure that a ball, initially at the lowest
point, will climb along a well defined meridian in the
rotating frame of reference (when the rpm goes up).

Any plane containing the axis of rotation is meridional. A
meridian is an intersection of such plane with the surface
of the dish; it does not have to be circular. Spherical
surfaces, however, are easier to create than parabolic.
Ludwik Kowalski

Robert A Cohen wrote:

> How about spinning a parabolic surface about its center?  At a particular
> rotation rate, a ball placed on its surface and at rest relative to the
> surface will stay stationary relative to the surface.  At this speed, the
> normal force (acting centripetally) will balance the centrifugal force
> (or, in other words, the normal force will be providing the centripetal
> force necessary for the ball to follow the circular path prescribed by the
> moving surface...whew!).  Thus, any motion relative to the surface will
> appear to be influenced by the coriolis force only (not the centrifugal
> force), as is the case with the geostrophic winds.
>
> If we drill a hole in the surface and attach the ball (that is residing on
> the surface) to an object that is free to hang down through the hole, the
> hanging bob will provide a force on the ball that will attract it to the
> hole, much like a low pressure center does on the atmosphere.  From the
> point of view of a camera mounted to rotate with the surface, the ball
> will appear to spiral around the hole, rather than go directly into it.
> This should be sufficient to demonstrate what you are looking for.
>
> By the way, the direction of the spiral will be the same direction
> (clockwise or counter-clockwise) as the spin of the surface.  From the
> "rest" frame, the stationary ball is spinning around the hole and so as it
> approaches the hole it spins faster, conserving angular momentum.