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色々な物体の慣性モーメント１
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色々な形の物体の、重心回りの慣性モーメントを一覧表にまとめてみました。物体の質量はどれも $M$ とします。図中に書き込まれた座標の原点は、物体の重心にあると思ってください。

一覧表
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.. csv-table:: 
   :header: "", "慣性モーメント", "図"

   "長さ $2a$ の細い棒"," $I_{z}=\frac{1}{3}Ma^2$ ", " .. image:: Joh-Inrt101.gif "
   "辺の長さが $2a \times 2b$ の長方形", " $ &I_{x}=\frac{1}{3}Mb^2 \\ &I_{y}=\frac{1}{3}Ma^2 \\ &I_{z}=\frac{1}{3}M(a^2 + b^2) $ ", " .. image:: Joh-Inrt102.gif "
   "半径 $a$ の薄円板", " $ &I_{z}=\frac{1}{2}Ma^2 \\ &I_{x}=I_{y}=\frac{1}{4}Ma^2$ ", " .. image:: Joh-Inrt105.gif" 
   "半径 $a$ の細い円輪"," $ &I_{z}=Ma^2 \\ &I_{x}=I_{y}=\frac{1}{2}Ma^2$ ", " .. image:: Joh-Inrt106.gif "
   "外半径 $a$ ,内半径 $b$ の中空円板"," $ &I_{z}=\frac{1}{2}(a^2+b^2)M \\ &I_{x}=I_{y}=\frac{1}{4}(a^2+b^2)M$ ", " .. image:: Joh-Inrt103.gif "
   "半径 $a$ の球"," $I=\frac{2}{5}Ma^2$ ", " .. image:: Joh-Inrt104.gif "
   "半径 $a$ の薄い球殻"," $I=\frac{2}{3}Ma^2$ ", " .. image:: Joh-Inrt104.gif "
   "外半径 $a$ ,内半径 $b$ の球殻"," $I=\frac{2(a^5-b^5)}{5(a^3-b^3)}M$ ", " .. image:: Joh-Inrt107.gif "
   "辺の長さが $2a \times 2b \times 2c$ の直方体"," $ &I_{x}=\frac{1}{3}(b^2+c^2)M \\ &I_{y}=\frac{1}{3}(c^2+a^2)M \\ &I_{z}=\frac{1}{3}(a^2+b^2)M $ ", " .. image:: Joh-Inrt108.gif "
   "半径 $a$ ,高さ $h$ の円柱"," $ &I_{z}=\frac{1}{2}Ma^2 \\ &I_{x}=I_{y}=\big( \frac{a^2}{2}+\frac{h^2}{12} \big) M$ ", " .. image:: Joh-Inrt109.gif "
      "半径 $a$ ,高さ $h$ の薄い中空円柱"," $I_{z}=Ma^2$ ", " .. image:: Joh-Inrt109.gif "
   "半径 $a$ の半球"," $ &I_{z}=\frac{2}{5}Ma^2 \\ &I_{x}=I_{y}=\frac{83}{320}Ma^2$ ", " .. image:: Joh-Inrt18.gif "
   "両軸が $2a$ , $2b$ の楕円形薄板"," $ &I_{x}=\frac{1}{4}Mb^2 \\ &I_{y}=\frac{1}{4}Ma^2 \\ &I_{z}=\frac{1}{4}(a^2+b^2)M $ ", " .. image:: Joh-Inrt20.gif "
   "両軸が $2a$ , $2b$ の楕円を底面とする高さ $h$ の楕円柱"," $ &I_{x}=\big( \frac{b^2}{4}+\frac{h^2}{12} \big) M \\ &I_{y}=\big (\frac{a^2}{4}+\frac{h^2}{12} \big) M \\ &I_{z}=\frac{1}{4}(a^2 + b^2) M$ ", " .. image:: Joh-Inrt110.gif "
   "三軸が $2a$ , $2b$ , $2c$ の楕円体"," $ &I_{x}=\frac{1}{5}(b^2 +c^2)M \\ &I_{y}=\frac{1}{5}(c^2 +a^2)M \\ &I_{z}=\frac{1}{5}(a^2 +b^2)M$ ", " .. image:: Joh-Inrt26.gif "
   "半径 $a$ の円を底面とし高さ $h$ の円錐"," $I_{z}=\frac{3}{10}Ma^2$ ", " .. image:: Joh-Inrt111.gif "
   "中心半径 $a$ , 管半径 $c$ のトーラス"," $ &I_{z}=\big( \frac{3}{4}a^2+c^2\big) M \\ &I_{x}=I_{y}=\frac{1}{8}\big( 5a^2+4c^2 \big)M$ ", " .. image:: Joh-Inrt112.gif "

   
   
   
   


.. _色々な物体の慣性モーメント２: 



@@author:Joh@@
@@accept: 2005-09-7@@