Re: A ball in a rotating dish (was Hot air rising ...)

[brian whatcott <inet@INTELLISYS.NET>]

At 06:44 9/12/99 -0400, Robert Cohen wrote:
> ... ask why the winds feel only a coriolis
> > force and not a centrifugal force.  ...ask how one
> > might roll a ball down a plane and have it *not* experience a coriolis
> > force (granted, the coriolis force would be small in any case, but there
> > is a way to get it to go to zero).
>
> 1. The winds do not "feel" the centrifugal force because ... the normal
> force (of the surface) has a slight centripetal component that cancels out
> the centrifugal force.  In other words, we define a horizontal surface as
> that surface for which there is no horizontal forces on an object at rest.
> That is, a horizontal surface is *not* the surface of a sphere.  If it
> was, everyone would be leaning slightly poleward (to counteract the
> centrifugal force) just as someone leans toward the center of the circle
> when walking in a circle.

 It is well to remember that we live on the surface of a globe that has
reacted to two long term terraforming forces - gravity and spin.
 consequently its surface figure is called an oblate spheroid.
Hence we ARE all leaning somewhat polewards at moderate latitudes.

 Coriolis effect is dynamic - it affects objects in motion. I am not
comfortable with the assertion that the normal force has a centripetal
component which counters a centrifugal force.

    In discussing surface friction, it is important to account for the
standard observation that the greater the surface roughness, the greater
the backing of the surface wind from its direction at moderate altitude
even where the surface is free to take up its surface of least potential
- over the oceans.

> 2. First some background...An object experiences a coriolis force when its
> distance from the earth's axis changes.  For example, if it moves toward
> the earth's axis, it will rotate faster than the earth (toward the east in
> the NH).  For an object moving horizontally in the northern hemisphere,
> the coriolis force will produce a deflection toward the right.  However,
> projectiles can be forced either to the right or left depending on their
> angle relative to horizontal.
>   Now the answer...To get no deflection at all, orient a board such that
> each part of the board is equidistant from the earth's axis. For example,
> for someone at 40 degrees N, the poleward end of the board would be higher
> than the equatorward end with the board making an angle of 40 degrees with
> the horizontal.  A ball that rolls down the inclined plane will not
> experience a coriolis force because its distance from the earth's axis
> does not change.

> | Robert Cohen

I expect Robert would assert that a cylindrical surface would not support
non tangential winds. So an easy experiment would be worth his
consideration:
take a cylindrical beaker and fill with water. Sprinkle with a powder of
 neutral density and add a magnetic stirrer.
 When stirred not shaken, an upwards circulation at the axis of revolution,
and downwards at the cylindrical wall is seen.



brian whatcott <inet@intellisys.net>
Altus OK