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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク List of area moments of inertia ： ウィキペディア英語版 List of area moments of inertia The following is a list of area moments of inertia. The Area Moment of Inertia or second moment of area has a unit of dimension length4, and should not be confused with the mass moment of inertia. If the piece is thin, however, the mass moment of inertia equals the area density times the area moment of inertia. Each is with respect to a horizontal axis through the centroid of the given shape, unless otherwise specified. ==Area moments of inertia== r^4 $I\_y\; =\; \backslash frac\; r^4$ $I\_z\; =\; \backslash frac\; r^4$|| ||〔(【引用サイトリンク】title=Circle )〕 |- | an annulus of inner radius ''r''1 and outer radius ''r''2||||$I\_x\; =\; \backslash frac\; \backslash left(^4-^4\backslash right)$ $I\_y\; =\; \backslash frac\; \backslash left(^4-^4\backslash right)$ $I\_z\; =\; \backslash frac\; \backslash left(^4-^4\backslash right)$|| For thin tubes, $r\; \backslash equiv\; r\_1\; \backslash approx\; r\_2$ and $r\_2\; \backslash equiv\; r\_1+t$. We can say that $\backslash left(r\_^4-r\_1^4\backslash right)\; =\; \backslash left(\backslash left(r\_1+t\backslash right)^4-r\_1^4\backslash right)\; =\; \backslash left(4r\_1^3t+6r\_1^2t^2+4r\_1t^3+t^4\backslash right)$ and because $r\_1>>t$ this bracket can be simplified to $\backslash left(4r\_1^3t+6r\_1^2t^2+4r\_1t^3+t^4\backslash right)\; \backslash approx\; 4r\_1^3t$. Ultimately, for a thin tube, $I\_x\; =\; I\_y\; =\; \backslash pi\; ^3$. || |- | a filled circular sector of angle ''θ'' in radians and radius ''r'' with respect to an axis through the centroid of the sector and the center of the circle||||$I\_0\; =\; \backslash left(\; \backslash theta\; -\backslash sin\; \backslash theta\; \backslash right)\; \backslash frac$||This formula is valid only for 0 ≤ $\backslash theta$ ≤ $\backslash pi$ || |- | a filled semicircle with radius ''r'' with respect to a horizontal line passing through the centroid of the area||||$I\_0\; =\; \backslash left(\backslash frac\; -\; \backslash frac\backslash right)r^4\; \backslash approx\; 0.1098r^4$|| ||〔(【引用サイトリンク】title=Circular Half )〕 |- | a filled semicircle as above but with respect to an axis collinear with the base||||$I\; =\; \backslash frac$||This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is $\backslash frac$||〔 |- | a filled semicircle as above but with respect to a vertical axis through the centroid||||$I\_0\; =\; \backslash frac$|| ||〔 |- | a filled quarter circle with radius ''r'' entirely in the 1st quadrant of the Cartesian coordinate system||||$I\; =\; \backslash frac$|| ||〔(【引用サイトリンク】title=Quarter Circle )〕 |- | a filled quarter circle as above but with respect to a horizontal or vertical axis through the centroid||||$I\_0\; =\; \backslash left(\backslash frac-\backslash frac\backslash right)r^4\; \backslash approx\; 0.0549r^4$||This is a consequence of the parallel axis theorem and the fact that the distance between these two axes is $\backslash frac$ ||〔 |- | a filled ellipse whose radius along the ''x''-axis is ''a'' and whose radius along the ''y''-axis is ''b''||

$I\_x\; =\; \backslash frac\; ab^3$ $I\_y\; =\; \backslash frac\; a^3b$|| || |- | a filled rectangular area with a base width of ''b'' and height ''h''||||$I\_x\; =\; \backslash frac$ $I\_y\; =\; \backslash frac$|| ||〔(【引用サイトリンク】title=Rectangular area )〕 |- | a filled rectangular area as above but with respect to an axis collinear with the base||||$I\; =\; \backslash frac$||This is a result from the parallel axis theorem||〔 |- | a filled rectangular area as above but with respect to an axis collinear, where ''r'' is the perpendicular distance from the centroid of the rectangle to the axis of interest|| ||$I\; =\; \backslash frac+bhr^2$||This is a result from the parallel axis theorem||〔 |- | a filled triangular area with a base width of ''b'' and height ''h'' with respect to an axis through the centroid||||$I\_0\; =\; \backslash frac$|| ||〔(【引用サイトリンク】title=Triangular area )〕 |- | a filled triangular area as above but with respect to an axis collinear with the base||||$I\; =\; \backslash frac$||This is a consequence of the parallel axis theorem ||〔 |- | a filled regular hexagon with a side length of ''a''||||$I\_0\; =\; \backslash fraca^4$||The result is valid for both a horizontal and a vertical axis through the centroid, and therefore is also valid for an axis with arbitrary direction that passes through the origin.|| |- | An equal legged angle||400x400px||$I\_x\; =\; I\_y\; =\; \backslash frac$ $I\_(xy)\; =\; \backslash frac$ $I\_a\; =\; \backslash frac$ $I\_b\; =\; \backslash frac$ || $I\_(xy)$ is the often unused product of inertia, used to define inertia with a rotated axis|| |- | Any plane region with a known area moment of inertia for a parallel axis. (Main Article parallel axis theorem) ||||$I\_z\; =\; I\_x\; +\; Ar^2$ || This can be used to determine the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of mass and the perpendicular distance (r) between the axes.|| |} 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「List of area moments of inertia」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.