{"id":456,"date":"2023-06-17T06:32:05","date_gmt":"2023-06-17T06:32:05","guid":{"rendered":"https:\/\/physigeek.com\/pt\/pendulo-simples\/"},"modified":"2023-06-17T06:32:05","modified_gmt":"2023-06-17T06:32:05","slug":"pendulo-simples","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/pendulo-simples\/","title":{"rendered":"P\u00eandulo simples"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 um p\u00eandulo simples e quais s\u00e3o suas caracter\u00edsticas. Tamb\u00e9m s\u00e3o apresentadas as f\u00f3rmulas que descrevem o movimento de um p\u00eandulo simples e, al\u00e9m disso, voc\u00ea poder\u00e1 ver quais s\u00e3o as leis do p\u00eandulo simples. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-un-pendulo-simple\"><\/span> O que \u00e9 um p\u00eandulo simples?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O <strong>p\u00eandulo simples<\/strong> , tamb\u00e9m chamado <strong>de p\u00eandulo matem\u00e1tico<\/strong> ou <strong>p\u00eandulo ideal<\/strong> , \u00e9 um sistema constitu\u00eddo por uma part\u00edcula de massa suspensa em um ponto fixo por meio de um fio de determinado comprimento.<\/p>\n<p> Na f\u00edsica, o p\u00eandulo simples \u00e9 usado para estudar o movimento oscilat\u00f3rio da massa suspensa. Se uma for\u00e7a for aplicada \u00e0 massa, ela oscilar\u00e1 al\u00e9m de sua posi\u00e7\u00e3o de equil\u00edbrio e, portanto, descrever\u00e1 um movimento oscilat\u00f3rio.<\/p>\n<p> Mais precisamente, o movimento realizado pela massa de um p\u00eandulo simples \u00e9 denominado <strong>movimento pendular<\/strong> , que \u00e9 <a href=\"https:\/\/physigeek.com\/pt\/movimento-periodico\/\">um movimento peri\u00f3dico<\/a> , pois a massa passa pela mesma posi\u00e7\u00e3o a cada intervalo de tempo fixo. <\/p>\n<div style=\"background-color:#FFFDE7; padding-top: 10px; padding-bottom: 10px; padding-right: 10px; padding-left: 20px; border: 2.5px dashed #FFB74D; border-radius:20px;\"> <span style=\"color:#ff951b\">\u27a4<\/span> <strong>Veja:<\/strong> <a href=\"https:\/\/physigeek.com\/pt\/movimento-do-pendulo\/\">O que \u00e9 movimento pendular?<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Caracteristicas-de-un-pendulo-simple\"><\/span> Caracter\u00edsticas de um p\u00eandulo simples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> O p\u00eandulo simples \u00e9 definido pelas seguintes caracter\u00edsticas ou partes:<\/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 simples 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 p\u00eandulo simples mais 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 necess\u00e1rio para completar 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 que o p\u00eandulo simples faz 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 vertical e pela corda do p\u00eandulo simples quando este est\u00e1 na posi\u00e7\u00e3o extrema.<\/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=\"caracter\u00edsticas de um p\u00eandulo simples, partes de um p\u00eandulo simples, elementos de um p\u00eandulo simples\" 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-pendulo-simple\"><\/span> F\u00f3rmulas de p\u00eandulo simples <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-diferencial-del-pendulo-simple\"><\/span> Equa\u00e7\u00e3o diferencial simples do p\u00eandulo<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> A equa\u00e7\u00e3o diferencial do p\u00eandulo simples 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 diferencial do p\u00eandulo simples<\/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-538fb79a964706dd993084143e043434_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\\cdot \\ddot{\\theta}+g\\cdot \\text{sen}(\\theta)=0\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"153\" 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 acelera\u00e7\u00e3o angular. <\/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<p> Se o p\u00eandulo simples fizer oscila\u00e7\u00f5es de pequena amplitude, a aproxima\u00e7\u00e3o sin(\u03b8)\u2248\u03b8 pode ser feita. Neste caso, a equa\u00e7\u00e3o diferencial do p\u00eandulo simples \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-ac8702a652711a416d848626edc80540_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\ell\\cdot \\ddot{\\theta}+g\\cdot \\theta=0\" title=\"Rendered by QuickLaTeX.com\" height=\"21\" width=\"114\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ecuacion-del-movimiento-del-pendulo-simple\"><\/span> Equa\u00e7\u00e3o do movimento de um p\u00eandulo simples<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Resolvendo a equa\u00e7\u00e3o diferencial vista na se\u00e7\u00e3o acima, chegamos \u00e0 equa\u00e7\u00e3o que descreve o \u00e2ngulo que o p\u00eandulo simples moveu em rela\u00e7\u00e3o \u00e0 sua posi\u00e7\u00e3o de equil\u00edbrio:<\/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-ee038d945fb195a2a70d1effc316d069_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\theta=\\Theta\\cdot\\text{sin}(\\omega\\cdot t+\\phi)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" 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-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 formado pela corda do p\u00eandulo simples e pela corda. <\/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-309d1e9dc1d3a46c23ed1f6d2449b454_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Theta\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a amplitude do p\u00eandulo simples. <\/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-fbffdce91996e0a17795d82e8e6996d9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a pulsa\u00e7\u00e3o ou frequ\u00eancia angular do p\u00eandulo simples. <\/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-fd9cb27edab3f0a8a249bc80cc9c6ee2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"6\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o instante em que o \u00e2ngulo \u00e9 calculado. <\/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-8358131e7f71b02f5a1b767b67603090_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\phi\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"11\" style=\"vertical-align: -4px;\"><\/p>\n<p> \u00e9 a fase inicial do p\u00eandulo simples.<\/span><\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Periodo-del-pendulo-simple\"><\/span> Per\u00edodo de p\u00eandulo simples<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Para pequenas oscila\u00e7\u00f5es, o per\u00edodo de oscila\u00e7\u00e3o de um p\u00eandulo simples \u00e9 igual a duas vezes pi vezes a raiz quadrada da raz\u00e3o 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 p\u00eandulo simples<\/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 p\u00eandulo simples. <\/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 simples. <\/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-pendulo-simple\"><\/span>Leis do p\u00eandulo simples<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Na f\u00edsica, existem quatro leis que definem o movimento oscilat\u00f3rio de um p\u00eandulo simples:<\/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 da massa<\/strong> : Dois p\u00eandulos cujas cordas t\u00eam o mesmo comprimento 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 de um p\u00eandulo simples \u00e9 independente da amplitude do movimento. Portanto, se dois p\u00eandulos simples 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 for o fio, maior ser\u00e1 o per\u00edodo 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 p\u00eandulo.<\/span><\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 um p\u00eandulo simples e quais s\u00e3o suas caracter\u00edsticas. Tamb\u00e9m s\u00e3o apresentadas as f\u00f3rmulas que descrevem o movimento de um p\u00eandulo simples e, al\u00e9m disso, voc\u00ea poder\u00e1 ver quais s\u00e3o as leis do p\u00eandulo simples. O que \u00e9 um p\u00eandulo simples? O p\u00eandulo simples , tamb\u00e9m chamado de p\u00eandulo matem\u00e1tico &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/pendulo-simples\/\"> <span class=\"screen-reader-text\">P\u00eandulo simples<\/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-456","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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