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 Available to Purchase
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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