Date: Sat, 17 Jan 1998 12:50:52 -0800
Message-Id: <v01520d00b0e6517cda65@[205.179.255.33]>
To: pinhole@exploratorium.edu
From: mafifi@redshift.com (Marc Afifi)
Subject: Re: Foucault Pendulums
>Hi Pinholers,
>My physics students are familiar with the Foucault pendulum at the Academy of
>Sciences, but they want to know if the pendulum makes a traverse of 360
>degrees in 24 hours. At the poles the pendulum should traverse 360 degrees.
Absolutely correct. Since at the poles it takes 24h for the Earth to rotate
beneath the pendulum.
>At the equator does it traverse zero degrees?
Yes. Because at the equator the pendulum feels a clockwise(?) torque as it
passes to the north of the equator and a counter-clockwise(?) torque when
it is south of the equator. These two torques exactly cancel out and no net
torque is experienced by the pendulum. So the pendulum remains in the same
plane. Paul Doherty has a good explanation of this using a book to
represent the plane of oscillation for the pendulum. Picture the book
perpendicular to the surface of the Earth and the pendulum oscillating in
the plane of the book. As the Earth falls away from the book due to the
Earth's rotation, the book is pulled toward the normal but the pendulum is
in motion so it experiences a torque which causes a rotation. (I'm still a
bit fuzzy about this one but it made sense when Paul explained it.)
>At latitudes in between is the rotation somewhere between zero and 360
>degrees,
>depending on the latitude? Anyone have an answer?
Again, yes. You are right on. I believe it takes 37h for one rotation in
SF, though my memory is fading with age. 24h at the poles, infinity at the
equator, somewhere in between depending on the latitude. Does anyone know
if there is a function which can be used to calculate the period depending
on the latitude?
Paul, does the orbit of the Earth around the Sun cause the pendulum to have
some finite period at the equator, say, for example, 365 days?
-mafifi
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