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zAbn8%nPNkjOj!#*vn+;;v^%f_`Fa*mCbg>3vQZ@1)?Jko*Rkf*q7XqW3I+etPUMi9 z6R!x;A#+JaRc?dZYhs#L=AY(9)(_K8A$9cJoz&2h$08Bpx>j(^^kgyaeu0Fxt`U_i z@pmz35EdZAH}gNlJ+|EKM|f?2qDq=j81|CgSK*Rt53ukjxH)j`j z4pSEwn3@8?s~$l>JV}^~B8~LF6bT0a1Oov8-2V&?_yPV8PjhEC%YT{xstSlm|5)L@ Oj`mlQZX^58?EeA#eP{{* diff --git a/Syllabus/chap_controle_rotation.tex b/Syllabus/chap_controle_rotation.tex index 1c971a3..9021328 100644 --- a/Syllabus/chap_controle_rotation.tex +++ b/Syllabus/chap_controle_rotation.tex @@ -8,8 +8,7 @@ Ceci concerne aussi bien les rotations transversales que longitudinales.\bigskip \subsection*{Moment d'inertie} \vspace{-0.4cm} \begin{definition} - Le moment d'inertie d'un corps quantifie la résistance de ce corps à une accélération angulaire (à sa mise en rotation). - % à une mise en rotation de ce solide (ou plus généralement à une accélération angulaire), et a pour dimension M·L² (le produit d'une masse et du carré d'une longueur, qui s'exprime en kg·m² dans le S.I.). + Le moment d'inertie d'un corps quantifie la résistance de ce corps à une accélération an\-gu\-lai\-re (à sa mise en rotation). \end{definition} \[\mybox{\vec{I} = m \times r^{2}}\] @@ -49,7 +48,7 @@ Voici un tableau récapitulatif des différents moments d'inertie (exprimés en \end{tabular} \end{table} -Ces moments d'inertie sont \textbf{approximatifs} : ils ont été calculés par l'auteur (\cite{frohlich79}) --qui n'était pas gymnaste-- sur son propre corps (avec une masse et un rayon propre). +Ces moments d'inertie sont \textbf{approximatifs} : ils ont été calculés par l'auteur (\cite{frohlich79}) sur son propre corps (avec une masse et un rayon propre). Ces chiffres ne sont donc pas représentatifs d'un gymnaste masculin et encore moins d'une gymnaste féminine. Ces valeurs ne doivent pas être connue par coeur.\bigskip @@ -93,15 +92,16 @@ Où : \item $\omega$ : vitesse angulaire (en rad/sec)\bigskip \end{itemize} -Or, comme nous l'avons vu, \underline{le moment cinétique $\vec{{\mathcal{L}}_c}$ d'un corps isolé ou pseudo-isolé reste constant}. -Cela a comme conséquence que seule la vitesse angulaire $\omega$ peut varier lorsque le moment d'inertie $\vec{I}$ change. +Or, comme nous l'avons vu, le moment cinétique $\vec{{\mathcal{L}}_c}$ d'un corps isolé ou pseudo-isolé est constant. +Ce\-la a comme conséquence que seule la vitesse angulaire $\omega$ peut varier lorsque le moment d'inertie $\vec{I}$ change. D'après la formule donc, la vitesse angulaire $\omega$ est inversement proportionnelle au moment d'inertie $\vec{I}$.\bigskip L'influence réciproque du moment d'inertie et de la vitesse angulaire peut être représentée sur un graphique. Vous pouvez observer ci-dessous la variation du moment d'inertie (de 20 à 1) et de la vitesse angulaire associée pour un moment cinétique constant de $20~kg.m^2$ : \begin{figure}[h!] \centering - \includegraphics[scale=0.5]{../img/graph_variation_I_omega.png} - \caption{Diminution du moment d'inertie (orange) et augmentation de la vitesse angulaire (bleu)} + % \includegraphics[scale=0.5]{../img/graph_variation_I_omega.png} + \includegraphics[scale=0.5]{../img/graph_variation_I_omega_2.png} + \caption{Diminution du moment d'inertie (bleu) et augmentation de la vitesse angulaire (orange)} \end{figure} Reprenons l'exemple du gymnaste réalisant un salto arrière. Lors d'un salto arrière tendu, si le gymnaste change de position et groupe, le moment d'inertie diminue et cette diminution provoquera donc une augmentation de la vitesse angulaire (accélération de la rotation).\bigskip diff --git a/Syllabus/layout_syllabus_ffg b/Syllabus/layout_syllabus_ffg index 591be86..ae42e39 160000 --- a/Syllabus/layout_syllabus_ffg +++ b/Syllabus/layout_syllabus_ffg @@ -1 +1 @@ -Subproject commit 591be86a1345114fa98aa0a1957965a4e27f1709 +Subproject commit ae42e39f0f7e3f8261f20c5ea12e74394ac57680