The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum

Detalhes bibliográficos
Autor(a) principal: Giacometti, Jose A. [UNESP]
Data de Publicação: 2020
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Institucional da UNESP
Texto Completo: http://dx.doi.org/10.1119/10.0000374
http://hdl.handle.net/11449/197333
Resumo: 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 (+/-omega(0) - Omega(z)), with omega(0) being the frequency of pendulum oscillation and Omega(z) 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. (C) 2020 American Association of Physics Teachers.
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spelling The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulumIn 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 (+/-omega(0) - Omega(z)), with omega(0) being the frequency of pendulum oscillation and Omega(z) 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. (C) 2020 American Association of Physics Teachers.Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)INEO (Brazil)Univ Sao Paulo, Inst Fis Sao Carlos, BR-13560590 Sao Carlos, SP, BrazilUniv Estadual Paulista, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP, BrazilUniv Estadual Paulista, Fac Ciencias & Tecnol, BR-19060900 Presidente Prudente, SP, BrazilAmer Inst PhysicsUniversidade de São Paulo (USP)Universidade Estadual Paulista (Unesp)Giacometti, Jose A. [UNESP]2020-12-10T20:13:46Z2020-12-10T20:13:46Z2020-04-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article292-297http://dx.doi.org/10.1119/10.0000374American Journal Of Physics. Melville: Amer Inst Physics, v. 88, n. 4, p. 292-297, 2020.0002-9505http://hdl.handle.net/11449/19733310.1119/10.0000374WOS:000522116800006Web of Sciencereponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengAmerican Journal Of Physicsinfo:eu-repo/semantics/openAccess2021-10-23T12:39:38Zoai:repositorio.unesp.br:11449/197333Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T13:31:42.813487Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false
dc.title.none.fl_str_mv The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
title The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
spellingShingle The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
Giacometti, Jose A. [UNESP]
title_short The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
title_full The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
title_fullStr The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
title_full_unstemmed The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
title_sort The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
author Giacometti, Jose A. [UNESP]
author_facet Giacometti, Jose A. [UNESP]
author_role author
dc.contributor.none.fl_str_mv Universidade de São Paulo (USP)
Universidade Estadual Paulista (Unesp)
dc.contributor.author.fl_str_mv Giacometti, Jose A. [UNESP]
description 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 (+/-omega(0) - Omega(z)), with omega(0) being the frequency of pendulum oscillation and Omega(z) 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. (C) 2020 American Association of Physics Teachers.
publishDate 2020
dc.date.none.fl_str_mv 2020-12-10T20:13:46Z
2020-12-10T20:13:46Z
2020-04-01
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://dx.doi.org/10.1119/10.0000374
American Journal Of Physics. Melville: Amer Inst Physics, v. 88, n. 4, p. 292-297, 2020.
0002-9505
http://hdl.handle.net/11449/197333
10.1119/10.0000374
WOS:000522116800006
url http://dx.doi.org/10.1119/10.0000374
http://hdl.handle.net/11449/197333
identifier_str_mv American Journal Of Physics. Melville: Amer Inst Physics, v. 88, n. 4, p. 292-297, 2020.
0002-9505
10.1119/10.0000374
WOS:000522116800006
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv American Journal Of Physics
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 292-297
dc.publisher.none.fl_str_mv Amer Inst Physics
publisher.none.fl_str_mv Amer Inst Physics
dc.source.none.fl_str_mv Web of Science
reponame:Repositório Institucional da UNESP
instname:Universidade Estadual Paulista (UNESP)
instacron:UNESP
instname_str Universidade Estadual Paulista (UNESP)
instacron_str UNESP
institution UNESP
reponame_str Repositório Institucional da UNESP
collection Repositório Institucional da UNESP
repository.name.fl_str_mv Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)
repository.mail.fl_str_mv
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