The motion of a conical pendulum in a rotating frame: The study of the paths, determination of oscillation periods, and the Bravais pendulum
Autor(a) principal: | |
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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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Repositório Institucional da UNESP |
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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 |
|
_version_ |
1808128242110955520 |