Re: "simple" pendulum

[Leigh Palmer <palmer@SFU.CA>]

At 5:40 AM -0700 8/5/99, Ludwik Kowalski wrote:
> Referring to:
>
> > > ... For example, in the rotating frame of reference the bob
> > > of a conical pendulum moves in a fixed plane (PHI=const).
>
> Leigh Palmer wrote:
>
> > That's incorrect. The bob of a conical pendulum is in
> > equilibrium, at rest, in the only rotating frame that
> > makes sense.
>
> I am sitting on a horizontal platform which rotates below
> the bob. The axis of rotation coincides with the line along
> which an inertial observer A would see the bob hanging
> in equilibrium. As far as I am concerned (observer B) the
> bob is swinging in the vertical plane. To me it is a simple
> pendulum to A it is a conical pendulum. The bob is not
> at rest in my frame, that frame makes sense to me.

I'll demur on playing the logical game based upon your
false premise. I think it arises from thinking about the
motion of the bob in the so-called "centrifugal potential".
I will try to clarify what I mean.

If you are thinking about a noncircular orbit for the bob
then that does not oscillate in a rotating plane either.
To conserve angular momentum with respect to the vertical
axis the bob must move with different angular velocities
at different distances from the axis, so it will be out-
of-plane for a constant angular velocity rotating frame
except at two points on its orbit in that frame. A
simple pendulum having angular velocity equal to the
angular frequency of the pendulum will have a figure eight
shape on the surface of a sphere when viewed from the
rotating frame.

I can't construct your case. A simple pendulum is not
possible in a rotating frame because centrifugal force
and gravity are not the only forces which act in that
frame. Because the bob is moving the Coriolis force acts
to push the bob out of the plane it would otherwise stay
in.

Leigh