{"id":439,"date":"2023-06-18T02:41:54","date_gmt":"2023-06-18T02:41:54","guid":{"rendered":"https:\/\/physigeek.com\/pt\/movimento-do-pendulo\/"},"modified":"2023-06-18T02:41:54","modified_gmt":"2023-06-18T02:41:54","slug":"movimento-do-pendulo","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/movimento-do-pendulo\/","title":{"rendered":"Movimento pendular"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 o movimento do p\u00eandulo na f\u00edsica e quais s\u00e3o suas caracter\u00edsticas. Da mesma forma, voc\u00ea encontrar\u00e1 exemplos do movimento do p\u00eandulo, as f\u00f3rmulas do movimento do p\u00eandulo e, finalmente, as quatro leis que definem o movimento de um p\u00eandulo. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-el-movimiento-pendular\"><\/span> O que \u00e9 movimento pendular?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>O movimento do p\u00eandulo<\/strong> \u00e9 o movimento realizado pela massa suspensa em um p\u00eandulo. Ou seja, o movimento pendular \u00e9 um movimento que descreve um corpo suspenso em uma base fixa que oscila de um lado para o outro.<\/p>\n<p> Por exemplo, o movimento feito por um rel\u00f3gio de p\u00eandulo \u00e9 um movimento de p\u00eandulo. Da mesma forma, o movimento feito por uma crian\u00e7a balan\u00e7ando e o movimento de um metr\u00f4nomo tamb\u00e9m s\u00e3o exemplos de movimentos pendulares.<\/p>\n<p> A principal caracter\u00edstica do movimento pendular \u00e9 ser um movimento peri\u00f3dico, pois a massa suspensa no p\u00eandulo realiza um movimento repetitivo. Assim, a massa oscila de um lado para o outro e passa pela mesma posi\u00e7\u00e3o a cada intervalo de tempo fixo.<\/p>\n<p> Esta condi\u00e7\u00e3o \u00e9 logicamente satisfeita se desprezarmos o atrito com o ar. Caso contr\u00e1rio, se levarmos em conta o atrito com o ar, o p\u00eandulo faria oscila\u00e7\u00f5es cada vez menores at\u00e9 parar completamente. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Elementos-del-movimiento-pendular\"><\/span> Elementos do movimento do p\u00eandulo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O movimento do p\u00eandulo \u00e9 composto pelos seguintes elementos:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Comprimento (\u2113)<\/strong> : \u00e9 o comprimento da corda que vai do ponto fixo do p\u00eandulo at\u00e9 o centro de gravidade do objeto que realiza o movimento do p\u00eandulo.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Oscila\u00e7\u00e3o<\/strong> : \u00e9 o arco percorrido pela massa entre as posi\u00e7\u00f5es extremas do movimento do p\u00eandulo mais o seu retorno \u00e0 posi\u00e7\u00e3o inicial.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Per\u00edodo (T)<\/strong> : \u00e9 o tempo que leva para fazer uma oscila\u00e7\u00e3o.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Frequ\u00eancia (f)<\/strong> : \u00e9 o n\u00famero de oscila\u00e7\u00f5es realizadas pelo movimento do p\u00eandulo por unidade de tempo.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u00c2ngulo (\u03b8)<\/strong> : \u00e9 o \u00e2ngulo formado pela corda do p\u00eandulo e pela vertical.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Amplitude (\u0398)<\/strong> : \u00e9 o \u00e2ngulo formado pela corda do p\u00eandulo quando ela est\u00e1 na posi\u00e7\u00e3o extrema e vertical.<\/span> <\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire.png\" alt=\"movimento do p\u00eandulo\" class=\"wp-image-8900\" width=\"430\" height=\"346\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire-300x242.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire-768x619.png 768w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/mouvement-pendulaire.png 910w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formulas-del-movimiento-pendular\"><\/span> F\u00f3rmulas de movimento pendular<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Veremos ent\u00e3o quais s\u00e3o as principais f\u00f3rmulas para o movimento do p\u00eandulo, quais s\u00e3o a equa\u00e7\u00e3o que descreve o movimento e a f\u00f3rmula que nos permite calcular o seu per\u00edodo de oscila\u00e7\u00e3o.<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-del-movimiento-pendular\"><\/span> Equa\u00e7\u00e3o do movimento do p\u00eandulo<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A equa\u00e7\u00e3o do movimento do p\u00eandulo afirma que a soma do comprimento da corda vezes a acelera\u00e7\u00e3o angular mais a acelera\u00e7\u00e3o da gravidade vezes o seno do \u00e2ngulo que a corda faz com a vertical \u00e9 igual a zero.<\/p>\n<p> Portanto, a <strong>equa\u00e7\u00e3o do movimento do p\u00eandulo<\/strong> \u00e9:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e3eee8079515e6f467ccb9b2cf3b3eeb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\\cdot \\ddot{\\theta}+g\\cdot \\text{sin}(\\theta)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"150\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a01f1555785d2234d4294020a2e3968a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o comprimento do p\u00eandulo. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-273485de50bb5d8bc82bf426ab9a4bec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ddot{\\theta}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a <a href=\"https:\/\/physigeek.com\/pt\/aceleracao-angular\/\">acelera\u00e7\u00e3o angular<\/a> . <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7b2034939b850e3311120fca462ab64e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o \u00e2ngulo que a corda do p\u00eandulo faz com a vertical. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e88010d25c51c0c42c505ee1004ed182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a acelera\u00e7\u00e3o da gravidade, cujo valor na Terra \u00e9 9,81 m\/s <sup>2<\/sup> . <\/span><\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Periodo-del-movimiento-pendular\"><\/span> Per\u00edodo do p\u00eandulo<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Para pequenas oscila\u00e7\u00f5es, o <a href=\"https:\/\/physigeek.com\/pt\/periodo-fisico\/\">per\u00edodo de oscila\u00e7\u00e3o<\/a> do movimento do p\u00eandulo \u00e9 igual a duas vezes pi vezes a raiz quadrada do quociente entre o comprimento da corda do p\u00eandulo e a acelera\u00e7\u00e3o da gravidade.<\/p>\n<p> Portanto, a <strong>f\u00f3rmula para calcular o per\u00edodo de oscila\u00e7\u00e3o de um movimento pendular<\/strong> com oscila\u00e7\u00f5es de pequena amplitude \u00e9 a seguinte:<\/p>\n<p class=\"has-text-align-center\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-49774e684263aae5d8703f86c9ed09b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle T=2\\pi\\sqrt{\\frac{\\ell}{g}}\" title=\"Rendered by QuickLaTeX.com\" height=\"54\" width=\"87\" style=\"vertical-align: -21px;\"><\/p>\n<\/p>\n<p style=\"margin-bottom:5px\"> Ouro: <\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-7e093fd43ad2c244140c11afe4d4bdff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"T\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o per\u00edodo do movimento do p\u00eandulo. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-a01f1555785d2234d4294020a2e3968a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o comprimento da corda do p\u00eandulo. <\/span><\/li>\n<li style=\"margin-bottom:5px\"><span style=\"color:#101010;font-weight: normal;\">\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/physigeek.com\/wp-content\/ql-cache\/quicklatex.com-e88010d25c51c0c42c505ee1004ed182_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"g\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a acelera\u00e7\u00e3o da gravidade, cujo valor na Terra \u00e9 9,81 m\/s <sup>2<\/sup> . <\/span><\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Leyes-del-movimiento-pendular\"><\/span>Leis do movimento do p\u00eandulo<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O movimento do p\u00eandulo \u00e9 definido pelas quatro leis a seguir:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Lei da independ\u00eancia de massa<\/strong> : dois p\u00eandulos cujas cordas medem a mesma medida t\u00eam o mesmo per\u00edodo independentemente da massa suspensa nas cordas. Em outras palavras, dois p\u00eandulos de massas diferentes ter\u00e3o o mesmo per\u00edodo se os comprimentos de suas cordas forem iguais.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Lei do isocronismo<\/strong> : o per\u00edodo do movimento do p\u00eandulo \u00e9 independente da amplitude do movimento. Assim, se dois p\u00eandulos tiverem o mesmo comprimento de corda, seus per\u00edodos ser\u00e3o equivalentes mesmo que suas amplitudes sejam diferentes.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Lei dos comprimentos<\/strong> : o per\u00edodo de oscila\u00e7\u00e3o de um movimento pendular \u00e9 proporcional ao comprimento da corda do p\u00eandulo. Assim, quanto maior o comprimento da corda, maior ser\u00e1 o per\u00edodo de movimento do p\u00eandulo.<\/span><\/li>\n<li style=\"margin-bottom:20px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>Lei das Acelera\u00e7\u00f5es da Gravidade<\/strong> : A acelera\u00e7\u00e3o da gravidade afeta o per\u00edodo de oscila\u00e7\u00e3o do movimento do p\u00eandulo, portanto o per\u00edodo de um p\u00eandulo mudar\u00e1 dependendo da gravidade do local. Quanto maior a gravidade, menor ser\u00e1 o per\u00edodo de oscila\u00e7\u00e3o do movimento do p\u00eandulo.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 o movimento do p\u00eandulo na f\u00edsica e quais s\u00e3o suas caracter\u00edsticas. Da mesma forma, voc\u00ea encontrar\u00e1 exemplos do movimento do p\u00eandulo, as f\u00f3rmulas do movimento do p\u00eandulo e, finalmente, as quatro leis que definem o movimento de um p\u00eandulo. O que \u00e9 movimento pendular? O movimento do p\u00eandulo \u00e9 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/movimento-do-pendulo\/\"> <span class=\"screen-reader-text\">Movimento pendular<\/span> Leia mais &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[3],"tags":[],"class_list":["post-439","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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