In this paper, Newton's equations are solved to describe the motion of a conical pendulum in a rotating frame for the right- and left-hand conical oscillations. If the pendulum is started with the initial angular velocity ( , being the frequency of pendulum oscillation and the angular velocity of the rotating frame around the z-axis, the paths are shown to be circular, which would apparently indicate that the Coriolis force becomes non-effective in the rotating frame. This paper explains why the paths in the rotating frame are circular, and the difference between the periods for the right- and left-handed rotations is calculated analytically. It is also shown that in an inertial frame, the conical pendulum follows an elliptical path. As the Bravais pendulum is a conical pendulum oscillating at Earth's surface, its motion is also discussed.
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April 2020
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April 01 2020
The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
José A. Giacometti
José A. Giacometti
Instituto de Física de São Carlos, Universidade de São Paulo
, 13560-590 – São Carlos, SP, Brazil
and Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista
, 19060-900 – Presidente Prudente, SP, Brazil
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José A. Giacometti
Instituto de Física de São Carlos, Universidade de São Paulo
, 13560-590 – São Carlos, SP, Brazil
and Faculdade de Ciências e Tecnologia, Universidade Estadual Paulista
, 19060-900 – Presidente Prudente, SP, Brazil
Am. J. Phys. 88, 292–297 (2020)
Article history
Received:
May 28 2019
Accepted:
November 28 2019
Citation
José A. Giacometti; The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum. Am. J. Phys. 1 April 2020; 88 (4): 292–297. https://doi.org/10.1119/10.0000374
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