Re: Hot air rising and automobile thermometers

[Leigh Palmer <palmer@SFU.CA>]

> When a skater brings his/her arms in and spins faster as a result, is it
> proper to say that the spin is driven by the inward force exerted by the
> skater on his/her arms?

I wouldn't say so. That is certainly the agency which is contributing
the additional kinetic energy, but the "spin" (if you mean the angular
momentum) is not driven at all since this force is not external to the
system and thus cannot change the angular momentum of the system.

> Before this discussion started, I would've said
> that it was proper.  Since I see the geostrophic winds as being similar
> and I also thought it proper to say that the pressure gradient was driving
> the winds.
>
> However, upon second thoughts, I think it might be *more* proper to say
> that the winds were "initially" driven by the pressure gradient force.

Yes; they are *initially* driven toward the low pressure center. As they
acquire greater speed they experience a Coriolis force in the direction
perpendicular to the inward radial motion, roughly parallel to the
isobar. The wind velocity increases and veers in that direction, toward
the right in the northern hemisphere. The Coriolis force (which is
always perpendicular to the velocity) changes by rotating to a direction
which more nearly opposes the pressure gradient force. The wind stops
accelerating when balance is achieved. (Of course we are neglecting the
motion in the larger picture. That is, of course, circulation in a
cyclone. The Coriolis force never gets quite as large as the pressure
gradient force.) We are left with a wind blowing in the direction of the
isobar. If we were to move with that wind we would find the lower
pressure to our left.

(The convention of describing a wind directed eastward as a "westerly"
has always annoyed me, but I use it without hesitation because the rest
of the world does so. It is a Good Thing that the convention is well
established; establishment of a single convention for what "vapor" and
"gas" mean would be similarly Good.)

> Perhaps it might be worthwhile to consider the following situation: if
> there exists only a x-dir force A, an object on the earth will speed up
> and eventually reach a constant speed in a direction perpendicular to the
> force at a constant speed.  The speed is constant and the net force is
> zero (force A balanced by coriolis force).  If the x-dir force suddenly
> disappears, the object would then start to follow a circular motion (only
> the coriolis force would be present).

Better, I think, would be the description of rotation of the velocity
and of the Coriolis force. I would be quite uncomfortable with any
"sudden disappearance" of a force.

> It seems weird to say that initial
> force A (which is no longer present) is still driving it.

> Does this sound better?

I think so.

Leigh