Message-Id: <l03102801b0e6ebd2086e@[156.1.196.5]>
In-Reply-To: <n1327127040.5175a@Tesla.exploratorium.edu>
Date: Sat, 17 Jan 1998 17:11:27 -0700
To: "Pinhole Listserv" <pinhole@exploratorium.edu>
From: Ron Wong <ronwong@inreach.com>
Subject: Re: Foucault Pendulum
>----------------------------------------------------------------------
>....
>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. At
>the equator does it traverse zero degrees? At latitudes in between is the
>rotation somewhere between zero and 360 degrees, depending on the latitude?
>Anyone have an answer?
>
>>Neil Fetter
Your students are on the right track regarding the behavior of the Foucault
Pendulum.
Normally, we think of the earth as an inertial frame of reference when it's
not.
Taking the earth's rotation into account, the matter becomes an issue of
one's frame of reference.
At the North pole, for instance, the earth's angular velocity is co-linear
with the vertical line that passes through the point of support of the
pendulum. As a result, the earth appears to rotate underneath the pendulum
in a counter-clockwise direction once every 24 hours. Of course, from the
earth's point of view, the pendulum's plane of swing will appear to rotate
clockwise once in 24 hours.
At the equator, the earth's angular velocity is perpendicular to the
vertical line that passes through the pendulum's point of support. Since
the angular velocity is perpendicular to the vertical, it has no component
along the vertical axis and thus the earth will no longer appear to rotate
underneath the pendulum. From the pendulum's point of view, the entire
earth is rotating once every 24 hours in a counter-clockwise direction
around a line perpendicular to the vertical at the point of support. From
the earth's point of view, the pendulum will just appear to be swinging
back and forth without any rotation in it's plane of swing.
If you want to find the period of the rotation of the pendulum's plane of
swing at any latitude, just use the following formula:
Period in hours = 24/sin(latitude in degrees).
Have fun. - ron