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

[Robert A Cohen <bbq@ESU.EDU>]

I was cleaning up my mail account and noticed a post I made a couple of
months ago in which I raised some questions but never bothered to answer
them.  For completeness, in case (or in the hope that) someone happens to
chance upon the questions (in the archive?) and wants to know the answers,
here they are.

First the questions...

> P.S. A good physics question is to ask why the winds feel only a coriolis
> force and not a centrifugal force.  Another good one is to 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 we 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.

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.

I apologize for the delay.  Feel free to delete if you are no longer
interested.  :)

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| Robert Cohen               Department of Physics       |
|                            East Stroudsburg University |
| bbq@esu.edu                East Stroudsburg, PA  18301 |
| http://www.esu.edu/~bbq/   (570) 422-3428              |
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