Classical Physics

   

Absolute Rotation Angle and Precession Rate of a Traveling Foucault Pendulum

Authors: Russell P. Patera

The time dependent absolute rotations of the Foucault Pendulum and its mounting fixture were derived for any latitude using attitude kinematics without relying on a detailed solution for the oscillatory motion of the pendulum bob. Employing a novel method to compute the associated solid angle, analytical solutions were found for both rotation angles and their time derivatives, as well as, the associated precession rate. The methodology was extended to a Foucault pendulum traveling across the Earth’s surface when the Earth spins at an arbitrary angular rate. When not translating across the Earth’s surface, both pendulum and its mounting fixture were found to have absolute rotation rates in the counterclockwise direction in the Northern Hemisphere. The difference in rotation rates is in agreement with the observed relative clockwise precession rate of the pendulum with respect to its mounting fixture. Unlike stationary pendulums, traveling pendulums generally have time varying precession rates. Numerical examples are presented for various cases involving stationary and moving Foucault Pendulums to illustrate the developed methods.

Comments: 27 Pages.

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Submission history

[v1] 2023-04-16 23:25:47

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