PSN-L Email List Message

Subject: Re: Ball Pivots
From: John & Jan Lahr johnjan@........
Date: Sun, 24 Nov 2002 17:33:50 -0700

Hi Randall,

Consider a circular magnet hanging from a horizontal iron bar:

(see: )

If the center of mass of the magnet is at its center, then there will be no
preferred position which could be considered an infinite period in terms of
a pendulum.

Next consider the situation with the center of mass on the edge of the

(see: )

The center of mass will rise a bit with rotation of the magnet, but not as much
as would a simple pendulum with length equal to the diameter of the magnet.
Thus the period is longer than the "equivalent" pendulum.

If a rod were connected to this magnet with a weight on it's end, then the
period will always be a bit longer than would be expected from the
pendulum with the length of the rod, but the longer the rod the less the
difference would be.

If the magnet were stuck to another magnet with the same diameter,
then the center of rotation would always be the center of the upper magnet.

If the lower pivot of a Lehman were designed to give the equivalent of
a very long boom, one would still be limited in the period if the upper
pivot remained a single point.  If both pivots worked with large round
surfaces running on parallel planar surfaces, then long periods could be
achieved without having to make the axis between the upper and=20 lower
pivots so nearly vertical.

I'm not really suggesting this as a viable mechanical arrangement,
but just as food for thought.


At 01:36 PM 11/23/2002, you wrote:
Hi All,
In pondering this issue, it would seem to me that as 2 convex surfaces roll, the contact point would move in the same direction as the mass.  This would put the pivot off center and effectively shorten the boom.  Depending on the radii involved the geometry with respect to the upper pivot will also be affected.  The effects would be magnified on a small instrument because the boom angles of motion for the same displacement will be larger.  In addition the small instrument is operating at a much finer angle between the upper and lower pivots so again the effect will be more pronounced.  Possibly the ball is more stable because the period is in effect lessening with displacement from center.  Any thoughts or calculations to either support or shoot me down?  I am using an archery point against an aircraft bolt head.  My FFT always has a peak between 18 and 25 seconds with very little adjustment needed.  I did go completely off the side when the river flooded 2 miles east of here and had to reset then and again when the water dropped.

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