{"id":393,"date":"2023-06-19T18:46:32","date_gmt":"2023-06-19T18:46:32","guid":{"rendered":"https:\/\/physigeek.com\/pt\/aceleracao-angular\/"},"modified":"2023-06-19T18:46:32","modified_gmt":"2023-06-19T18:46:32","slug":"aceleracao-angular","status":"publish","type":"post","link":"https:\/\/physigeek.com\/pt\/aceleracao-angular\/","title":{"rendered":"Acelera\u00e7\u00e3o angular"},"content":{"rendered":"<p>Este artigo explica o que \u00e9 acelera\u00e7\u00e3o angular na f\u00edsica. Assim, voc\u00ea descobrir\u00e1 como calcular a acelera\u00e7\u00e3o angular, um exerc\u00edcio resolvido e qual a rela\u00e7\u00e3o entre acelera\u00e7\u00e3o angular e acelera\u00e7\u00e3o tangencial. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%C2%BFQue-es-la-aceleracion-angular\"><\/span> O que \u00e9 acelera\u00e7\u00e3o angular?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>A acelera\u00e7\u00e3o angular<\/strong> \u00e9 uma medida que define a acelera\u00e7\u00e3o rotacional de um corpo. Portanto, a acelera\u00e7\u00e3o angular indica a mudan\u00e7a na velocidade angular de um corpo. Em outras palavras, a acelera\u00e7\u00e3o angular representa a taxa na qual a velocidade angular muda.<\/p>\n<p> A unidade de acelera\u00e7\u00e3o angular no Sistema Internacional (SI) \u00e9 o radiano por segundo ao quadrado (rad\/s <sup>2<\/sup> ). Da mesma forma, a acelera\u00e7\u00e3o angular tamb\u00e9m \u00e9 expressa em unidades de s <sup>-2<\/sup> , uma vez que o radiano \u00e9, na verdade, adimensional.<\/p>\n<p> A acelera\u00e7\u00e3o angular \u00e9 geralmente representada pelo s\u00edmbolo da letra grega \u03b1 (alfa). <\/p>\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\/acceleration-angulaire.png\" alt=\"acelera\u00e7\u00e3o angular\" class=\"wp-image-7362\" width=\"357\" height=\"249\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/acceleration-angulaire-300x210.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/acceleration-angulaire.png 493w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\n<p> A acelera\u00e7\u00e3o angular \u00e9 representada por um vetor axial paralelo ao eixo de rota\u00e7\u00e3o. A norma do vetor \u00e9 o valor da acelera\u00e7\u00e3o angular e a dire\u00e7\u00e3o do vetor \u00e9 determinada pela regra da m\u00e3o direita. No plano, se o objeto girar no sentido hor\u00e1rio, o vetor de acelera\u00e7\u00e3o angular ir\u00e1 para dentro do plano, por outro lado, se o objeto girar no sentido anti-hor\u00e1rio, o vetor de acelera\u00e7\u00e3o angular ir\u00e1 para fora do plano. <\/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\/velocidade-angular\/\">Como encontrar a velocidade angular<\/a> <\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Formula-de-la-aceleracion-angular\"><\/span> F\u00f3rmula de acelera\u00e7\u00e3o angular<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A acelera\u00e7\u00e3o angular m\u00e9dia \u00e9 igual ao aumento da velocidade angular (\u0394\u03c9) dividido pelo aumento do tempo (\u0394t). Assim, para calcular a acelera\u00e7\u00e3o angular, a diferen\u00e7a entre a velocidade angular final e inicial deve ser dividida pela diferen\u00e7a entre o instante final e inicial (\u03b1 = \u0394\u03c9\/\u0394t).<\/p>\n<p> Portanto, a <strong>f\u00f3rmula para calcular a acelera\u00e7\u00e3o m\u00e9dia<\/strong> \u00e9: <\/p>\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\/formule-dacceleration-angulaire.png\" alt=\"f\u00f3rmula de acelera\u00e7\u00e3o angular\" class=\"wp-image-7365\" width=\"232\" height=\"231\" srcset=\"https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire-300x300.png 300w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire-150x150.png 150w, https:\/\/physigeek.com\/wp-content\/uploads\/2023\/09\/formule-dacceleration-angulaire.png 414w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\"><\/figure>\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-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" 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-94f4e26a511e85d1ab00d3f1686bf7e8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta \\omega\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"26\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a mudan\u00e7a na velocidade 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-819ab50990df5adf82bea9dfa75ffff2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\Delta t\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"21\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 a varia\u00e7\u00e3o temporal. <\/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-562a49afd4fa3e0e36dd810290074f64_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_f\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"19\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u00e9 a velocidade angular final. <\/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-90b8586302c2fbf8bfa7a04162507ebd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\omega_i\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"16\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a velocidade angular inicial. <\/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-82d36af17e232807e56da9ccdbbda0d8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_f\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"14\" style=\"vertical-align: -6px;\"><\/p>\n<p> \u00e9 o momento final. <\/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-bf289b768173104db12fe7044c723db4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t_i\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"11\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 o momento inicial.<\/span><\/li>\n<\/ul>\n<p> Tenha em mente que esta f\u00f3rmula s\u00f3 \u00e9 cumprida se o m\u00f3bile descrever um movimento circular uniformemente acelerado, ou seja, se a acelera\u00e7\u00e3o angular for constante ao longo do percurso. Caso contr\u00e1rio, use a seguinte f\u00f3rmula para encontrar a <strong>acelera\u00e7\u00e3o angular instant\u00e2nea<\/strong> :<\/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-9ca4f14fe6b21fc84c313375224fb893_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle\\alpha=\\lim_{\\Delta t\\to0}\\frac{\\Delta\\omega}{\\Delta t}=\\frac{d\\omega}{dt}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"152\" style=\"vertical-align: -13px;\"><\/p>\n<\/p>\n<p> Ap\u00f3s calcular o valor da acelera\u00e7\u00e3o angular, o resultado deve ser interpretado de acordo com o sinal da acelera\u00e7\u00e3o angular:<\/p>\n<ul style=\"color:#4fd12f; font-weight: bold;\">\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1&gt;0<\/strong> : se a acelera\u00e7\u00e3o angular for positiva, isso significa que o valor da velocidade angular aumenta com o tempo. \u00c9, portanto, um movimento circular uniformemente acelerado.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1&lt;0<\/strong> : se a acelera\u00e7\u00e3o angular for negativa, significa que o valor da velocidade angular diminui com o tempo. \u00c9, portanto, um movimento circular uniformemente retardado.<\/span><\/li>\n<li style=\"margin-bottom:16px\"> <span style=\"color:#101010;font-weight: normal;\"><strong>\u03b1=0<\/strong> : se a acelera\u00e7\u00e3o angular for igual a zero, isso significa que o valor da velocidade angular \u00e9 constante. \u00c9, portanto, um movimento circular uniforme.<\/span> <\/li>\n<\/ul>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Ejemplo-del-calculo-de-la-aceleracion-angular\"><\/span> Exemplo de c\u00e1lculo de acelera\u00e7\u00e3o angular<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Depois de ver a defini\u00e7\u00e3o de acelera\u00e7\u00e3o angular e sua f\u00f3rmula, nesta se\u00e7\u00e3o veremos um exemplo concreto de como a acelera\u00e7\u00e3o angular \u00e9 calculada.<\/p>\n<ul>\n<li> Um corpo em movimento circular gira com velocidade angular de 80 rpm. Se ap\u00f3s 6 segundos ele parar de girar completamente, qual ser\u00e1 a acelera\u00e7\u00e3o angular m\u00e9dia do corpo durante esse per\u00edodo?<\/li>\n<\/ul>\n<p> Primeiro, converteremos a velocidade angular em radianos por segundo para trabalhar com unidades do Syst\u00e8me International. Uma volta \u00e9 igual a 2\u03c0 radianos, ent\u00e3o:<\/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-84da1ead9b143fa4e97b6539717d9788_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"80 \\ \\cfrac{tours}{min} \\cdot \\cfrac{2\\pi \\ rad}{1 \\ tour}\\cdot \\cfrac{1 \\ min}{60 \\ s}=8,38 \\ \\cfrac {rad }{s}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"291\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Agora aplicamos a f\u00f3rmula da acelera\u00e7\u00e3o angular:<\/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-fedefe7f3708477dc61b93a792509ab6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=\\cfrac{\\Delta\\omega}{\\Delta t}=\\cfrac{\\omega_f-\\omega_i}{t_f-t_i}\" title=\"Rendered by QuickLaTeX.com\" height=\"45\" width=\"148\" style=\"vertical-align: -18px;\"><\/p>\n<\/p>\n<p> Quando o corpo finalmente parar, a velocidade angular final ser\u00e1 zero. Al\u00e9m disso, n\u00e3o sabemos o valor do instante final ou do instante inicial, mas sabemos que a diferen\u00e7a entre os dois \u00e9 de 6 s. A acelera\u00e7\u00e3o angular \u00e9 portanto:<\/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-fde4a41d03c719f8f5fd9b007a0f2387_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha=\\cfrac{0-8.38}{6}=-1.40 \\ \\cfrac{rad}{s^2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"204\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Observe que neste caso a acelera\u00e7\u00e3o angular \u00e9 negativa, o que significa que o corpo gira a uma velocidade angular cada vez mais lenta at\u00e9 parar completamente. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Aceleracion-angular-y-aceleracion-tangencial\"><\/span> Acelera\u00e7\u00e3o angular e acelera\u00e7\u00e3o tangencial<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> A acelera\u00e7\u00e3o angular e a acelera\u00e7\u00e3o tangencial est\u00e3o matematicamente relacionadas, portanto a acelera\u00e7\u00e3o tangencial pode ser calculada a partir da acelera\u00e7\u00e3o angular (ou vice-versa).<\/p>\n<p> A acelera\u00e7\u00e3o tangencial (ou acelera\u00e7\u00e3o linear) \u00e9 calculada multiplicando a acelera\u00e7\u00e3o angular pelo raio da trajet\u00f3ria do movimento circular. Portanto, a acelera\u00e7\u00e3o angular e a acelera\u00e7\u00e3o tangencial est\u00e3o relacionadas pelo raio da trajet\u00f3ria do movimento circular.<\/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-dcadf85fe24bbd678ca72ce3e1f0e582_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_t=\\alpha\\cdot r\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"71\" style=\"vertical-align: -3px;\"><\/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-ab56b4b3337ead2a6dab40b537d0ba6c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a_t\" title=\"Rendered by QuickLaTeX.com\" height=\"11\" width=\"14\" style=\"vertical-align: -3px;\"><\/p>\n<p> \u00e9 a acelera\u00e7\u00e3o tangencial. <\/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-5f44d9bbc8046069be4aa2989bff19aa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\alpha\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"11\" 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-01bcf7e9e043561da78fecf715c8a46e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> \u00e9 o raio da trajet\u00f3ria do movimento circular. <\/span><\/li>\n<\/ul>\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\/aceleracao-tangencial-ou-aceleracao-linear\/\">O que \u00e9 acelera\u00e7\u00e3o tangencial?<\/a><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Este artigo explica o que \u00e9 acelera\u00e7\u00e3o angular na f\u00edsica. Assim, voc\u00ea descobrir\u00e1 como calcular a acelera\u00e7\u00e3o angular, um exerc\u00edcio resolvido e qual a rela\u00e7\u00e3o entre acelera\u00e7\u00e3o angular e acelera\u00e7\u00e3o tangencial. O que \u00e9 acelera\u00e7\u00e3o angular? A acelera\u00e7\u00e3o angular \u00e9 uma medida que define a acelera\u00e7\u00e3o rotacional de um corpo. Portanto, a acelera\u00e7\u00e3o angular indica &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/physigeek.com\/pt\/aceleracao-angular\/\"> <span class=\"screen-reader-text\">Acelera\u00e7\u00e3o angular<\/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-393","post","type-post","status-publish","format-standard","hentry","category-cinematografico"],"yoast_head":"<!-- This site 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