Dimensions Physiques, Unit\u00e9s et Grandeurs Observables<\/title> <\/p>\n<style>\n table {\n display: block;\n overflow: scroll;\n }\n <\/style>\n<\/head><body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\"> <center> <\/p>\n<h1>Dimensions Physiques, Unit\u00e9s et Grandeurs Observables<\/h1>\nR\u00e9sum\u00e9 :<\/strong> \n Dans cette classe, vous apprendrez \u00e0 diff\u00e9rencier les grandeurs fondamentales telles que la masse, la longueur et le temps, et comment elles sont reli\u00e9es aux unit\u00e9s d\u00e9riv\u00e9es telles que l’aire et la force. Vous d\u00e9couvrirez l’importance des grandeurs observables comparables dans les lois de l’alg\u00e8bre et comment convertir les unit\u00e9s entre diff\u00e9rents syst\u00e8mes de mesure. Cette classe couvre \u00e9galement les grandeurs vectorielles, essentielles pour la formulation des \u00e9quations physiques, vous pr\u00e9parant \u00e0 une compr\u00e9hension plus profonde de la mesure en sciences.\n <\/p>\nINDEX DES CONTENUS<\/strong><\/u> \n <a href=\"#1\">Quelles sont les unit\u00e9s et les dimensions physiques ?<\/a> \n <a href=\"#2\">Unit\u00e9s fondamentales, d\u00e9riv\u00e9es et leurs dimensions physiques<\/a> \n <a href=\"#3\">Observables, grandeurs et unit\u00e9s physiques<\/a> \n <a href=\"#4\">Alg\u00e8bre des observables comparables<\/a> \n <a href=\"#5\">Lectures Recommand\u00e9es<\/a>\n <\/p>\n <\/center> \n <center> \n <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/WmhuV7rxL_0\" title=\"Lecteur vid\u00e9o YouTube\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe> \n <\/center>\n <\/div>\n<a name=\"1\"><\/a><\/p>\n<h2>Quelles sont les unit\u00e9s et les dimensions physiques?<\/h2>\nD\u00e9finir pr\u00e9cis\u00e9ment ce qu’est une dimension physique<\/strong> peut \u00eatre complexe. Cependant, nous pouvons comprendre que la physique s’occupe de grandeurs qui peuvent \u00eatre mesur\u00e9es. Ces grandeurs physiques<\/strong> sont class\u00e9es selon leur dimension<\/strong> et sont quantifi\u00e9es par comparaison avec des unit\u00e9s<\/strong> standards. Il existe deux cat\u00e9gories principales d’unit\u00e9s : les unit\u00e9s fondamentales<\/strong>, telles que le m\u00e8tre ou le kilogramme, et les unit\u00e9s d\u00e9riv\u00e9es<\/strong>, qui sont form\u00e9es \u00e0 partir des unit\u00e9s fondamentales par des op\u00e9rations alg\u00e9briques. Le tableau suivant pr\u00e9sente certaines des unit\u00e9s fondamentales et leurs dimensions physiques correspondantes.<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Dimensions Physiques<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Symbole dimensionnel<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Unit\u00e9 fondamentale<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Symbole de l’unit\u00e9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Masse<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">M<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kilogramme<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kg<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Longueur<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">L<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">m\u00e8tre<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">m<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Temps<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">T<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">seconde<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">s<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Intensit\u00e9 de courant \u00e9lectrique<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">I<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">amp\u00e8re<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">A<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\"><a href=\"https:\/\/toposuranos.com\/tag\/temperatura\/\" target=\"_blank\" rel=\"noopener\">Temp\u00e9rature Thermodynamique<\/a><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">\\Theta<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kelvin<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">K<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\"><a href=\"https:\/\/toposuranos.com\/tag\/mol\/\" target=\"_blank\" rel=\"noopener\">Quantit\u00e9 de substance<\/a><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">N<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">mole<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">mol<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Intensit\u00e9 lumineuse<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">I_v<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">candela<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">cd<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nC’est une erreur commune d’associer directement les grandeurs physiques aux dimensions physiques. Cette association est valable pour les grandeurs mesur\u00e9es avec des unit\u00e9s fondamentales telles que la masse ou le temps. Cependant, pour les grandeurs utilisant des unit\u00e9s d\u00e9riv\u00e9es, comme la force, la relation n’est pas directe. Par exemple, la force n’a pas sa propre dimension ; au contraire, elle se compose d’autres dimensions de base.<\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>Unit\u00e9s fondamentales, d\u00e9riv\u00e9es et leurs dimensions physiques<\/h2>\nChaque unit\u00e9 fondamentale correspond \u00e0 une seule dimension physique, telle que la masse, la longueur ou le temps. Les dimensions des unit\u00e9s d\u00e9riv\u00e9es r\u00e9sultent du produit alg\u00e9brique des dimensions des unit\u00e9s fondamentales. Voici quelques exemples :<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>L’aire<\/strong> est le r\u00e9sultat du produit de deux longueurs et donc sa dimension est L^2<\/span>, mesurable en m\u00e8tres carr\u00e9s (m^2<\/span>).<\/li>\n<li>Le volume<\/strong>, obtenu de trois longueurs ou d’une aire multipli\u00e9e par une longueur, a une dimension de L^3<\/span> et est mesur\u00e9 en m\u00e8tres cubes (m^3<\/span>).<\/li>\n<li>La vitesse<\/strong>, d\u00e9finie comme la distance divis\u00e9e par le temps, a une dimension de LT^{-1}<\/span> et est exprim\u00e9e en m\u00e8tres par seconde (m\/s<\/span>).<\/li>\n<li>L’acc\u00e9l\u00e9ration<\/strong> est calcul\u00e9e comme la vitesse divis\u00e9e par le temps, avec une dimension de LT^{-2}<\/span> et est mesur\u00e9e en m\u00e8tres par seconde carr\u00e9e (m\/s^2<\/span>).<\/li>\n<li>La force<\/strong> est le r\u00e9sultat du produit de la masse par l’acc\u00e9l\u00e9ration, donnant lieu \u00e0 une dimension de MLT^{-2}<\/span>. Elle est couramment mesur\u00e9e en Newtons (N<\/span>), repr\u00e9sent\u00e9e par la formule :\n\\displaystyle N = \\frac{kg \\cdot m}{s^2}<\/span>\n<\/li>\n<\/ul>\nDe mani\u00e8re similaire, de nombreuses autres grandeurs et dimensions physiques peuvent \u00eatre d\u00e9riv\u00e9es.<\/p>\n<a name=\"3\"><\/a><\/p>\n<h2>Observables, Grandeurs et Unit\u00e9s Physiques<\/h2>\nNous continuerons \u00e0 d\u00e9velopper les concepts que nous avons introduits. Nous appelons grandeur observable<\/strong>, ou simplement \u00abobservable\u00bb, toute propri\u00e9t\u00e9 ou ph\u00e9nom\u00e8ne qui peut \u00eatre mesur\u00e9, tel que la couleur, la longueur, le temps, le volume ou la duret\u00e9.<\/p>\nLes observables se divisent en deux cat\u00e9gories : les comparables et les non-comparables. Sont des observables comparables<\/strong> ceux qui peuvent \u00e9tablir une relation quantitative, par exemple, lorsque la longueur d’une poutre est plusieurs fois celle d’un crayon. En revanche, nous ne pouvons pas quantifier comparativement la couleur ; ainsi, alors que la longueur est un observable comparable, la couleur est non comparable.<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>Alg\u00e8bre des Observables Comparables<\/h2>\nLa logique derri\u00e8re les observables comparables est bas\u00e9e sur des principes d’\u00e9galit\u00e9 et d’addition :<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>Crit\u00e8re d’\u00c9galit\u00e9 :<\/strong> Deux observables comparables sont \u00e9gaux si le quotient de l’un par l’autre est \u00e9gal \u00e0 un (\\frac{A}{B} = 1<\/span>).<\/li>\n<li>Crit\u00e8re d’Addition :<\/strong> Si nous avons trois observables comparables A<\/span>, B<\/span> et C<\/span> en relation avec un quatri\u00e8me O<\/span>, et que les proportions \\frac{A}{O} = n_1<\/span>, \\frac{B}{O} = n_2<\/span> et \\frac{C}{O} = n_3<\/span> sont remplies, alors nous disons que A + B = C<\/span> si et seulement si n_1 + n_2 = n_3<\/span>.<\/li>\n<\/ul>\nAvec ces principes, il est d\u00e9montr\u00e9 que les observables comparables suivent les lois alg\u00e9briques d’associativit\u00e9, de distributivit\u00e9 et de commutativit\u00e9.<\/p>\n<h3>Unit\u00e9s de Mesure et Grandeurs Physiques<\/h3>\nUne unit\u00e9 de mesure<\/strong> est un observable comparable s\u00e9lectionn\u00e9 pour \u00e9tablir des comparaisons avec d’autres observables de la m\u00eame dimension. Si deux observables, A<\/span> et U_A<\/span>, sont comparables, il existe un nombre r\u00e9el \\alpha<\/span> tel que A<\/span> est \u00e9gal \u00e0 \\alpha<\/span> fois l’unit\u00e9 de mesure U_A<\/span>.<\/p>\nA = \\alpha U_A<\/span>\nPar exemple, si la longueur d’une poutre est de 3 m\u00e8tres, nous \u00e9crivons que la longueur de la poutre est 3 [m]<\/span>. La grandeur d’une mesure varie en fonction du syst\u00e8me d’unit\u00e9s utilis\u00e9, ce qui implique que la poutre mesurant 3<\/span> m\u00e8tres aura une grandeur approximative de 118.11<\/span> si elle est mesur\u00e9e en pouces.<\/p>\n<h3>Transformation des Unit\u00e9s de Mesure<\/h3>\nComme nous l’avons vu, nous pouvons mesurer un observable dans diff\u00e9rentes unit\u00e9s tant qu’elles partagent la m\u00eame dimension. Si A<\/span> est un observable, et U_1<\/span> et U_2<\/span> sont deux unit\u00e9s de mesure de la m\u00eame dimension, il existera deux nombres r\u00e9els \\alpha_1<\/span> et \\alpha_2<\/span> correspondants.<\/p>\nA = \\alpha_1 U_1<\/span> et A = \\alpha_2 U_2<\/span>\nPar cons\u00e9quent, le facteur de conversion \\gamma^2_1 = \\alpha_2 \/ \\alpha_1<\/span> permet de transformer l’unit\u00e9 U_2<\/span> en U_1<\/span>, et vice versa avec \\gamma^1_2 = \\alpha_1 \/ \\alpha_2<\/span>. Par exemple, une tige mesurant 5<\/span> pouces de longueur \u00e9quivaut \u00e0 0.127<\/span> m\u00e8tres, ce qui nous donne un facteur de conversion de 0.0254<\/span> m\u00e8tres par pouce.<\/p>\n<h3>Grandeurs Vectorielles<\/h3>\nNous avons examin\u00e9 des observables d\u00e9crits par une seule grandeur. Cependant, il existe des observables tels que la position dans l’espace qui n\u00e9cessitent plusieurs grandeurs pour une description compl\u00e8te. Ceux-ci sont connus comme des grandeurs vectorielles<\/strong> et sont repr\u00e9sent\u00e9s par plusieurs valeurs. Par exemple, un objet situ\u00e9 \u00e0 3<\/span> m\u00e8tres vers la droite, 5<\/span> m\u00e8tres vers l’avant et 2<\/span> m\u00e8tres vers le haut est repr\u00e9sent\u00e9 comme (3, 5, 2)<\/span> m\u00e8tres.<\/p>\n{position} = (3, 5, 2)<\/span>\nCes grandeurs b\u00e9n\u00e9ficient de l’alg\u00e8bre vectorielle, ce qui simplifie leur manipulation et leur application dans les formules physiques. Un exemple courant est la force, repr\u00e9sent\u00e9e comme un vecteur ayant une grandeur et une direction, essentielle dans de nombreuses \u00e9quations physiques.<\/p>\n<h2>Lectures Recommand\u00e9es<\/h2>\nSyst\u00e8me International de Poids et Mesures : <a href=\"https:\/\/www.cem.es\/sites\/default\/files\/siu8edes.pdf\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/www.cem.es\/sites\/default\/files\/siu8edes.pdf<\/a><\/p>\nGuide for the Use of the International System of Units (SI) : <a href=\"https:\/\/physics.nist.gov\/cuu\/pdf\/sp811.pdf\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/physics.nist.gov\/cuu\/pdf\/sp811.pdf<\/a><\/p>\nSyst\u00e8me anglais d’unit\u00e9s : <a href=\"https:\/\/web.archive.org\/web\/20060427072134\/http:\/\/encyclopedie-es.snyke.com\/articles\/sistema_ingles.html\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/web.archive.org\/web\/20060427072134\/http:\/\/encyclopedie-es.snyke.com\/articles\/sistema_ingles.html<\/a><\/p>\n<\/body> \n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"Dimensions Physiques, Unit\u00e9s et Grandeurs Observables Dimensions Physiques, Unit\u00e9s et Grandeurs Observables R\u00e9sum\u00e9 : Dans cette classe, vous apprendrez \u00e0 diff\u00e9rencier les grandeurs fondamentales telles que la masse, la longueur et le temps, et comment elles sont reli\u00e9es aux unit\u00e9s d\u00e9riv\u00e9es telles que l’aire et la force. Vous d\u00e9couvrirez l’importance des grandeurs observables comparables dans […]<\/p>\n","protected":false},"author":1,"featured_media":25219,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":25,"footnotes":""},"categories":[663,647],"tags":[],"citadela-post-location":[],"class_list":["post-25217","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fondements-de-la-mecanique","category-physique"],"yoast_head":"\n<title>Dimensions Physiques, Unit\u00e9s et Grandeurs Observables - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Avec cette classe, vous ma\u00eetriserez les concepts de dimensions et de grandeurs physiques. \ud83d\udd0dD\u00e9couvrez comment mesurer les grandeurs fondamentales.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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{"id":25217,"date":"2021-08-12T00:00:53","date_gmt":"2021-08-12T00:00:53","guid":{"rendered":"http:\/\/toposuranos.com\/material\/?p=25217"},"modified":"2024-05-21T09:42:54","modified_gmt":"2024-05-21T09:42:54","slug":"dimensions-physiques-unites-et-grandeurs-observables","status":"publish","type":"post","link":"https:\/\/toposuranos.com\/material\/fr\/dimensions-physiques-unites-et-grandeurs-observables\/","title":{"rendered":"Dimensions Physiques, Unit\u00e9s et Grandeurs Observables"},"content":{"rendered":"

\n Dimensions Physiques, Unit\u00e9s et Grandeurs Observables<\/title> <\/p>\n<style>\n table {\n display: block;\n overflow: scroll;\n }\n <\/style>\n<\/head><body> <\/p>\n<div style=\"background-color:#F3F3F3; padding:20px;\"> <center> <\/p>\n<h1>Dimensions Physiques, Unit\u00e9s et Grandeurs Observables<\/h1>\nR\u00e9sum\u00e9 :<\/strong> \n Dans cette classe, vous apprendrez \u00e0 diff\u00e9rencier les grandeurs fondamentales telles que la masse, la longueur et le temps, et comment elles sont reli\u00e9es aux unit\u00e9s d\u00e9riv\u00e9es telles que l’aire et la force. Vous d\u00e9couvrirez l’importance des grandeurs observables comparables dans les lois de l’alg\u00e8bre et comment convertir les unit\u00e9s entre diff\u00e9rents syst\u00e8mes de mesure. Cette classe couvre \u00e9galement les grandeurs vectorielles, essentielles pour la formulation des \u00e9quations physiques, vous pr\u00e9parant \u00e0 une compr\u00e9hension plus profonde de la mesure en sciences.\n <\/p>\nINDEX DES CONTENUS<\/strong><\/u> \n <a href=\"#1\">Quelles sont les unit\u00e9s et les dimensions physiques ?<\/a> \n <a href=\"#2\">Unit\u00e9s fondamentales, d\u00e9riv\u00e9es et leurs dimensions physiques<\/a> \n <a href=\"#3\">Observables, grandeurs et unit\u00e9s physiques<\/a> \n <a href=\"#4\">Alg\u00e8bre des observables comparables<\/a> \n <a href=\"#5\">Lectures Recommand\u00e9es<\/a>\n <\/p>\n <\/center> \n <center> \n <iframe class=\"lazyload\" width=\"560\" height=\"315\" data-src=\"https:\/\/www.youtube.com\/embed\/WmhuV7rxL_0\" title=\"Lecteur vid\u00e9o YouTube\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen=\"allowfullscreen\"><\/iframe> \n <\/center>\n <\/div>\n<a name=\"1\"><\/a><\/p>\n<h2>Quelles sont les unit\u00e9s et les dimensions physiques?<\/h2>\nD\u00e9finir pr\u00e9cis\u00e9ment ce qu’est une dimension physique<\/strong> peut \u00eatre complexe. Cependant, nous pouvons comprendre que la physique s’occupe de grandeurs qui peuvent \u00eatre mesur\u00e9es. Ces grandeurs physiques<\/strong> sont class\u00e9es selon leur dimension<\/strong> et sont quantifi\u00e9es par comparaison avec des unit\u00e9s<\/strong> standards. Il existe deux cat\u00e9gories principales d’unit\u00e9s : les unit\u00e9s fondamentales<\/strong>, telles que le m\u00e8tre ou le kilogramme, et les unit\u00e9s d\u00e9riv\u00e9es<\/strong>, qui sont form\u00e9es \u00e0 partir des unit\u00e9s fondamentales par des op\u00e9rations alg\u00e9briques. Le tableau suivant pr\u00e9sente certaines des unit\u00e9s fondamentales et leurs dimensions physiques correspondantes.<\/p>\n<table style=\"color: #000000;\">\n<tbody>\n<tr>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Dimensions Physiques<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Symbole dimensionnel<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Unit\u00e9 fondamentale<\/td>\n<td style=\"text-align: center; background-color: #000000; color: #ffffff;\">Symbole de l’unit\u00e9<\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Masse<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">M<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kilogramme<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kg<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Longueur<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">L<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">m\u00e8tre<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">m<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Temps<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">T<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">seconde<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">s<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Intensit\u00e9 de courant \u00e9lectrique<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">I<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">amp\u00e8re<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">A<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\"><a href=\"https:\/\/toposuranos.com\/tag\/temperatura\/\" target=\"_blank\" rel=\"noopener\">Temp\u00e9rature Thermodynamique<\/a><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">\\Theta<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">kelvin<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">K<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\"><a href=\"https:\/\/toposuranos.com\/tag\/mol\/\" target=\"_blank\" rel=\"noopener\">Quantit\u00e9 de substance<\/a><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">N<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">mole<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">mol<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center; background-color: #ffffff;\">Intensit\u00e9 lumineuse<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">I_v<\/span><\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">candela<\/td>\n<td style=\"text-align: center; background-color: #ffffff;\">cd<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\nC’est une erreur commune d’associer directement les grandeurs physiques aux dimensions physiques. Cette association est valable pour les grandeurs mesur\u00e9es avec des unit\u00e9s fondamentales telles que la masse ou le temps. Cependant, pour les grandeurs utilisant des unit\u00e9s d\u00e9riv\u00e9es, comme la force, la relation n’est pas directe. Par exemple, la force n’a pas sa propre dimension ; au contraire, elle se compose d’autres dimensions de base.<\/p>\n<a name=\"2\"><\/a><\/p>\n<h2>Unit\u00e9s fondamentales, d\u00e9riv\u00e9es et leurs dimensions physiques<\/h2>\nChaque unit\u00e9 fondamentale correspond \u00e0 une seule dimension physique, telle que la masse, la longueur ou le temps. Les dimensions des unit\u00e9s d\u00e9riv\u00e9es r\u00e9sultent du produit alg\u00e9brique des dimensions des unit\u00e9s fondamentales. Voici quelques exemples :<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>L’aire<\/strong> est le r\u00e9sultat du produit de deux longueurs et donc sa dimension est L^2<\/span>, mesurable en m\u00e8tres carr\u00e9s (m^2<\/span>).<\/li>\n<li>Le volume<\/strong>, obtenu de trois longueurs ou d’une aire multipli\u00e9e par une longueur, a une dimension de L^3<\/span> et est mesur\u00e9 en m\u00e8tres cubes (m^3<\/span>).<\/li>\n<li>La vitesse<\/strong>, d\u00e9finie comme la distance divis\u00e9e par le temps, a une dimension de LT^{-1}<\/span> et est exprim\u00e9e en m\u00e8tres par seconde (m\/s<\/span>).<\/li>\n<li>L’acc\u00e9l\u00e9ration<\/strong> est calcul\u00e9e comme la vitesse divis\u00e9e par le temps, avec une dimension de LT^{-2}<\/span> et est mesur\u00e9e en m\u00e8tres par seconde carr\u00e9e (m\/s^2<\/span>).<\/li>\n<li>La force<\/strong> est le r\u00e9sultat du produit de la masse par l’acc\u00e9l\u00e9ration, donnant lieu \u00e0 une dimension de MLT^{-2}<\/span>. Elle est couramment mesur\u00e9e en Newtons (N<\/span>), repr\u00e9sent\u00e9e par la formule :\n\\displaystyle N = \\frac{kg \\cdot m}{s^2}<\/span>\n<\/li>\n<\/ul>\nDe mani\u00e8re similaire, de nombreuses autres grandeurs et dimensions physiques peuvent \u00eatre d\u00e9riv\u00e9es.<\/p>\n<a name=\"3\"><\/a><\/p>\n<h2>Observables, Grandeurs et Unit\u00e9s Physiques<\/h2>\nNous continuerons \u00e0 d\u00e9velopper les concepts que nous avons introduits. Nous appelons grandeur observable<\/strong>, ou simplement \u00abobservable\u00bb, toute propri\u00e9t\u00e9 ou ph\u00e9nom\u00e8ne qui peut \u00eatre mesur\u00e9, tel que la couleur, la longueur, le temps, le volume ou la duret\u00e9.<\/p>\nLes observables se divisent en deux cat\u00e9gories : les comparables et les non-comparables. Sont des observables comparables<\/strong> ceux qui peuvent \u00e9tablir une relation quantitative, par exemple, lorsque la longueur d’une poutre est plusieurs fois celle d’un crayon. En revanche, nous ne pouvons pas quantifier comparativement la couleur ; ainsi, alors que la longueur est un observable comparable, la couleur est non comparable.<\/p>\n<a name=\"4\"><\/a><\/p>\n<h2>Alg\u00e8bre des Observables Comparables<\/h2>\nLa logique derri\u00e8re les observables comparables est bas\u00e9e sur des principes d’\u00e9galit\u00e9 et d’addition :<\/p>\n<ul style=\"text-align: justify; color: #000000;\">\n<li>Crit\u00e8re d’\u00c9galit\u00e9 :<\/strong> Deux observables comparables sont \u00e9gaux si le quotient de l’un par l’autre est \u00e9gal \u00e0 un (\\frac{A}{B} = 1<\/span>).<\/li>\n<li>Crit\u00e8re d’Addition :<\/strong> Si nous avons trois observables comparables A<\/span>, B<\/span> et C<\/span> en relation avec un quatri\u00e8me O<\/span>, et que les proportions \\frac{A}{O} = n_1<\/span>, \\frac{B}{O} = n_2<\/span> et \\frac{C}{O} = n_3<\/span> sont remplies, alors nous disons que A + B = C<\/span> si et seulement si n_1 + n_2 = n_3<\/span>.<\/li>\n<\/ul>\nAvec ces principes, il est d\u00e9montr\u00e9 que les observables comparables suivent les lois alg\u00e9briques d’associativit\u00e9, de distributivit\u00e9 et de commutativit\u00e9.<\/p>\n<h3>Unit\u00e9s de Mesure et Grandeurs Physiques<\/h3>\nUne unit\u00e9 de mesure<\/strong> est un observable comparable s\u00e9lectionn\u00e9 pour \u00e9tablir des comparaisons avec d’autres observables de la m\u00eame dimension. Si deux observables, A<\/span> et U_A<\/span>, sont comparables, il existe un nombre r\u00e9el \\alpha<\/span> tel que A<\/span> est \u00e9gal \u00e0 \\alpha<\/span> fois l’unit\u00e9 de mesure U_A<\/span>.<\/p>\nA = \\alpha U_A<\/span>\nPar exemple, si la longueur d’une poutre est de 3 m\u00e8tres, nous \u00e9crivons que la longueur de la poutre est 3 [m]<\/span>. La grandeur d’une mesure varie en fonction du syst\u00e8me d’unit\u00e9s utilis\u00e9, ce qui implique que la poutre mesurant 3<\/span> m\u00e8tres aura une grandeur approximative de 118.11<\/span> si elle est mesur\u00e9e en pouces.<\/p>\n<h3>Transformation des Unit\u00e9s de Mesure<\/h3>\nComme nous l’avons vu, nous pouvons mesurer un observable dans diff\u00e9rentes unit\u00e9s tant qu’elles partagent la m\u00eame dimension. Si A<\/span> est un observable, et U_1<\/span> et U_2<\/span> sont deux unit\u00e9s de mesure de la m\u00eame dimension, il existera deux nombres r\u00e9els \\alpha_1<\/span> et \\alpha_2<\/span> correspondants.<\/p>\nA = \\alpha_1 U_1<\/span> et A = \\alpha_2 U_2<\/span>\nPar cons\u00e9quent, le facteur de conversion \\gamma^2_1 = \\alpha_2 \/ \\alpha_1<\/span> permet de transformer l’unit\u00e9 U_2<\/span> en U_1<\/span>, et vice versa avec \\gamma^1_2 = \\alpha_1 \/ \\alpha_2<\/span>. Par exemple, une tige mesurant 5<\/span> pouces de longueur \u00e9quivaut \u00e0 0.127<\/span> m\u00e8tres, ce qui nous donne un facteur de conversion de 0.0254<\/span> m\u00e8tres par pouce.<\/p>\n<h3>Grandeurs Vectorielles<\/h3>\nNous avons examin\u00e9 des observables d\u00e9crits par une seule grandeur. Cependant, il existe des observables tels que la position dans l’espace qui n\u00e9cessitent plusieurs grandeurs pour une description compl\u00e8te. Ceux-ci sont connus comme des grandeurs vectorielles<\/strong> et sont repr\u00e9sent\u00e9s par plusieurs valeurs. Par exemple, un objet situ\u00e9 \u00e0 3<\/span> m\u00e8tres vers la droite, 5<\/span> m\u00e8tres vers l’avant et 2<\/span> m\u00e8tres vers le haut est repr\u00e9sent\u00e9 comme (3, 5, 2)<\/span> m\u00e8tres.<\/p>\n{position} = (3, 5, 2)<\/span>\nCes grandeurs b\u00e9n\u00e9ficient de l’alg\u00e8bre vectorielle, ce qui simplifie leur manipulation et leur application dans les formules physiques. Un exemple courant est la force, repr\u00e9sent\u00e9e comme un vecteur ayant une grandeur et une direction, essentielle dans de nombreuses \u00e9quations physiques.<\/p>\n<h2>Lectures Recommand\u00e9es<\/h2>\nSyst\u00e8me International de Poids et Mesures : <a href=\"https:\/\/www.cem.es\/sites\/default\/files\/siu8edes.pdf\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/www.cem.es\/sites\/default\/files\/siu8edes.pdf<\/a><\/p>\nGuide for the Use of the International System of Units (SI) : <a href=\"https:\/\/physics.nist.gov\/cuu\/pdf\/sp811.pdf\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/physics.nist.gov\/cuu\/pdf\/sp811.pdf<\/a><\/p>\nSyst\u00e8me anglais d’unit\u00e9s : <a href=\"https:\/\/web.archive.org\/web\/20060427072134\/http:\/\/encyclopedie-es.snyke.com\/articles\/sistema_ingles.html\" rel=\"nofollow, noreferrer, noopener\" target=\"_blank\">https:\/\/web.archive.org\/web\/20060427072134\/http:\/\/encyclopedie-es.snyke.com\/articles\/sistema_ingles.html<\/a><\/p>\n<\/body> \n<\/html><\/p>\n","protected":false},"excerpt":{"rendered":"Dimensions Physiques, Unit\u00e9s et Grandeurs Observables Dimensions Physiques, Unit\u00e9s et Grandeurs Observables R\u00e9sum\u00e9 : Dans cette classe, vous apprendrez \u00e0 diff\u00e9rencier les grandeurs fondamentales telles que la masse, la longueur et le temps, et comment elles sont reli\u00e9es aux unit\u00e9s d\u00e9riv\u00e9es telles que l’aire et la force. Vous d\u00e9couvrirez l’importance des grandeurs observables comparables dans […]<\/p>\n","protected":false},"author":1,"featured_media":25219,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"iawp_total_views":25,"footnotes":""},"categories":[663,647],"tags":[],"citadela-post-location":[],"class_list":["post-25217","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-fondements-de-la-mecanique","category-physique"],"yoast_head":"\n<title>Dimensions Physiques, Unit\u00e9s et Grandeurs Observables - toposuranos.com\/material<\/title>\n<meta name=\"description\" content=\"Avec cette classe, vous ma\u00eetriserez les concepts de dimensions et de grandeurs physiques. \ud83d\udd0dD\u00e9couvrez comment mesurer les grandeurs fondamentales.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" 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