翻訳と辞書 Words near each other ・ Stretch fabric ・ Stretch factor ・ Stretch four ・ Stretch Island ・ Stretch Johnson ・ Stretch Kontelj ・ Stretch marks ・ Stretch Murphy ・ Stretch Number 1 ・ Stretch Panic ・ Stretch Point State Park ・ Stretch Princess ・ Stretch receptor ・ Stretch Records ・ Stretch reflex ・ Stretch rule ・ Stretch Screamers ・ Stretch shortening cycle ・ Stretch tents ・ Stretch That Skull Cover and Smile ・ Stretch wrap ・ Stretch-activated ion channel ・ Stretchable electronics ・ Stretched C ・ Stretched exponential function ・ Stretched grid method ・ Stretched Rohini Satellite Series ・ Stretched tuning ・ Stretched verb ・ Stretcher Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Stretch rule ： ウィキペディア英語版 Stretch rule In physics, the stretch rule (sometimes referred to as Routh's rule) states that the moment of inertia of a rigid object is unchanged when the object is stretched parallel to an axis of rotation that is a principal axis, provided that the distribution of mass remains unchanged except in the direction parallel to the axis. This operation leaves cylinders oriented parallel to the axis unchanged in radius. This rule can be applied with the parallel axis theorem and the perpendicular axes rule to find moments of inertia for a variety of shapes. ==Derivation== The (scalar) moment of inertia of a rigid body around the z-axis is given by: :$I\_z\; =\; \backslash int\_V\; d^3\; r\; \backslash ,\; \backslash rho(\backslash mathbf)\backslash ,r^2$ Where $r$ is the distance of a point from the z-axis. We can expand as follows, since we are dealing with stretching over the z-axis only: :$I\_z\; =\; \backslash int\_^\; dz\; \backslash int\_\; dx\; dy\; \backslash ,\; \backslash rho(x,\; y,\; z)\backslash ,r^2$ Here, $L$ is the body's height. Stretching the object by a factor of $a$ along the z-axis is equivalent to dividing the mass density by $a$ (meaning $\backslash rho\text{'}(x,\; y,\; z)\; =\; \backslash rho(x,\; y,\; z/a)/a$), as well as integrating over new limits $0$ and $aL$ (the new height of the object), thus leaving the total mass unchanged. This means the new moment of inertia will be: :$I\_\text{'}\; =\; \backslash int\_^\; dz\; \backslash int\_\; dx\; dy\; \backslash ,\; \backslash rho\text{'}(x,\; y,\; z)\; \backslash ,r^2$ ::$=\; \backslash int\_^\; adz\text{'}\; \backslash int\_\; dx\; dy\; \backslash ,\; \backslash frac\; \backslash ,r^2$ ::$=\; \backslash int\_^\; dz\text{'}\; \backslash int\_\; dx\; dy\; \backslash ,\; \backslash rho(x,\; y,\; z\text{'})\; \backslash ,r^2\; =\; I\_z$ 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「Stretch rule」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.