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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 Centripetal force ： ウィキペディア英語版 Centripetal force A centripetal force (from Latin ''centrum'' "center" and ''petere'' "to seek"〔, (Extract of page 291 )〕) is a force that makes a body follow a curved path. Its direction is always orthogonal to the motion of the body and towards the fixed point of the instantaneous center of curvature of the path. Isaac Newton described it as "a force by which bodies are drawn or impelled, or in any way tend, towards a point as to a centre." In Newtonian mechanics, gravity provides the centripetal force responsible for astronomical orbits. One common example involving centripetal force is the case in which a body moves with uniform speed along a circular path. The centripetal force is directed at right angles to the motion and also along the radius towards the centre of the circular path.〔 〕 The mathematical description was derived in 1659 by Dutch physicist Christiaan Huygens.〔 〕 == Formula == The magnitude of the centripetal force on an object of mass ''m'' moving at tangential speed ''v'' along a path with radius of curvature ''r'' is: :$F\; =\; ma\_c\; =\; \backslash frac$ where $a\_c$ is the centripetal acceleration. The direction of the force is toward the center of the circle in which the object is moving, or the osculating circle (the circle that best fits the local path of the object, if the path is not circular).〔 〕 The speed in the formula is squared, so twice the speed needs four times the force. The inverse relationship with the radius of curvature shows that half the radial distance requires twice the force. This force is also sometimes written in terms of the angular velocity ''ω'' of the object about the center of the circle, related to the tangential velocity by the formula :$v\; =\; \backslash omega\; r$ so that :$F\; =\; m\; r\; \backslash omega^2\; \backslash ,.$ Expressed using the orbital period ''T'' for one revolution of the circle, :$\backslash omega\; =\; \backslash frac\; \backslash ,.$ the equation becomes :$F\; =\; m\; r\; \backslash left(\backslash frac\backslash right)^2$ In particle accelerators, velocity can be very high (close to the speed of light in vacuum) so the same rest mass now exerts greater inertia (relativistic mass) thereby requiring greater force for the same centripetal acceleration, so the equation becomes: :$F\; =\; \backslash frac$ where :$\backslash gamma\; =\; \backslash frac\{\backslash sqrt\{1-v^2/c^2\}\}$ is called the Lorentz factor. 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「Centripetal force」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.