Median absolute deviation - Revision history

en>Tipusalman87: /* Relation to standard deviation */

2014-12-08T20:29:25Z

Relation to standard deviation

← Older revision		Revision as of 22:29, 8 December 2014
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	~~In physics, the~~ '~~''perpendicular axis theorem''' (or '''plane figure theorem''') can be used to determine the [[moment~~ of ~~inertia]] of a~~ [[rigid object]] that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two [[perpendicular]] [[Coordinate axis\|axes]] lying within the plane. ~~The axes must all pass through a single point in the plane~~.		Hello friend. Allow me introduce myself. I am Ron but I don't like when individuals use my complete title. One of his preferred [http://www.continentalwarranty.org/ hobbies] is playing [http://nationalheritagemuseum.org/UserProfile/tabid/43/userId/31686/Default.aspx auto warranty] crochet but he hasn't made a dime with it. His [http://sticker-shocked.com/UserProfile/tabid/43/userId/404/Default.aspx extended auto warranty] day occupation is a financial officer but he plans on [http://www.bankrate.com/finance/auto/automakers-best-car-warranties-1.aspx extended auto] warranty changing it. I currently live in Arizona but extended car warranty now [http://Www.Allstate.com/tools-and-resources/car-insurance/whats-in-a-new-car-warranty.aspx I'm contemplating] other options.<br><br>Visit my homepage [http://glskating.com/groups/great-ideas-about-auto-repair-that-you-can-use/ extended car warranty]

	~~Define perpendicular axes <math>x\,<~~/~~math>, <math>y\,<~~/~~math>, and <math>z\,<~~/~~math> (which meet at origin <math>O\,<~~/~~math>) so that the body lies in the <math>xy\,<~~/~~math> plane, and the <math>z\,<~~/~~math> axis is perpendicular to the plane of the body. Let ''I''<sub>''x''<~~/~~sub>, ''I''<sub>''y''<~~/~~sub> and ''I''<sub>''z''<~~/~~sub> be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that<ref>{{cite book \|title=Physics \|author=Paul A~~. ~~Tipler \|chapter=Ch~~. 12: ~~Rotation of a Rigid Body about a Fixed Axis \|publisher=Worth Publishers Inc~~. ~~\|isbn=0-87901-041-X \|year=1976}}<~~/~~ref>~~

	~~:<math>I_z = I_x + I_y\,<~~/~~math>~~

	~~This rule can be applied with the [[parallel axis theorem~~]~~] and the [[stretch rule]] to find moments of inertia for~~ a ~~variety of shapes.~~

	~~If a planar object (or prism, by the~~ [~~[stretch rule]]) has rotational symmetry such that <math>I_x\,</math> and <math>I_y\,</math> are equal, then the perpendicular axes theorem provides the useful relationship:~~

	:~~<math>I_z = 2I_x = 2I_y\,<~~/~~math>~~

	~~== Derivation ==~~
	~~Working in Cartesian co-ordinates, the moment of inertia of the planar body about the <math>z\,<~~/~~math> axis is given by:<ref>{{cite book \|title=Mathematical Methods for Physics and Engineering \|author=K~~. F. ~~Riley, M~~. P. ~~Hobson & S~~. J. ~~Bence \|chapter=Ch. 6: Multiple Integrals \|publisher=Cambridge University Press \|isbn=978~~-0-~~521~~-~~67971~~-~~8 \|year=2006}}~~<~~/ref~~>

	:<~~math~~>~~I_{z} = \int \left(x^2 + y^2\right)\, dm = \int x^2\,dm + \int y^2\,dm = I_{y} + I_{x} <~~/~~math>~~

	~~On the plane, <math>z=0\,<~~/~~math>, so these two terms are the moments of inertia about the <math>x\,<~~/~~math> and <math>y\,<~~/~~math> axes respectively, giving the perpendicular axis theorem.~~
	~~The converse of this theorem is also derived similarly.~~

	~~Note~~ that ~~<math>\int x^2\,dm = I_{y} \ne I_{x} </math> because in <math>\int r^2\,dm </math>, r measures the distance from the ''axis of rotation'', so for a y~~-~~axis rotation, deviation distance from the axis of rotation of a point is equal to its x co~~-~~ordinate.~~

	~~== References ==~~
	~~{{reflist}}~~

	~~==See also==~~
	* [[Parallel axis theorem]]
	* [[Stretch rule]]

	~~{{DEFAULTSORT:Perpendicular Axis Theorem}}~~
	~~[[Category:Rigid bodies]]~~
	~~[[Category:Physics theorems]]~~
	~~[[Category:Articles containing proofs]]~~
	~~[[Category:Classical mechanics]~~]

103.27.8.43: the example violated the definition. looked like a typing error. http://reference.wolfram.com/mathematica/ref/MedianDeviation.html

2014-01-28T06:59:36Z

the example violated the definition. looked like a typing error. http://reference.wolfram.com/mathematica/ref/MedianDeviation.html

← Older revision		Revision as of 08:59, 28 January 2014
Line 1:		Line 1:
	~~Hello~~, ~~my name is~~ [~~http://Www.angieslist.com/articles/what-does-and-doesnt-your-auto-warranty-cover.htm Felicidad~~] ~~but I~~ [~~http://www~~.~~claysculpturesbydon~~.~~com~~/~~UserProfile~~/~~tabid~~/~~170~~/~~userId~~/~~5546~~/~~Default~~.~~aspx extended car warranty]~~ ~~[http:~~//~~www~~.~~jvawest.com/UserProfile/tabid/152/userId/2157/Default~~.~~aspx extended auto warranty] car warranty don't like when [http~~:~~//www~~.~~Wikihow.com/Buy~~-an-~~Extended~~-~~Warranty-for-a-Car individuals~~] ~~use my complete title. Some time ago he selected to reside in Idaho. She functions as a financial officer~~ and ~~she will not change it anytime soon. The favorite pastime for him and his kids is~~ to ~~play badminton but he is struggling to car warranty~~ find ~~time~~ for it.<br><br>~~Also visit my site~~ :: ~~[http:~~//~~Beyoufirst~~.~~org~~/~~ActivityFeed~~/~~MyProfile~~/~~tabid~~/62/~~userId~~/~~31300~~/~~Default~~.~~aspx extended car warranty~~]		In physics, the '''perpendicular axis theorem''' (or '''plane figure theorem''') can be used to determine the [[moment of inertia]] of a [[rigid object]] that lies entirely within a plane, about an axis perpendicular to the plane, given the moments of inertia of the object about two [[perpendicular]] [[Coordinate axis\|axes]] lying within the plane. The axes must all pass through a single point in the plane.

			Define perpendicular axes <math>x\,</math>, <math>y\,</math>, and <math>z\,</math> (which meet at origin <math>O\,</math>) so that the body lies in the <math>xy\,</math> plane, and the <math>z\,</math> axis is perpendicular to the plane of the body. Let ''I''<sub>''x''</sub>, ''I''<sub>''y''</sub> and ''I''<sub>''z''</sub> be moments of inertia about axis x, y, z respectively, the perpendicular axis theorem states that<ref>{{cite book \|title=Physics \|author=Paul A. Tipler \|chapter=Ch. 12: Rotation of a Rigid Body about a Fixed Axis \|publisher=Worth Publishers Inc. \|isbn=0-87901-041-X \|year=1976}}</ref>

			:<math>I_z = I_x + I_y\,</math>

			This rule can be applied with the [[parallel axis theorem]] and the [[stretch rule]] to find moments of inertia for a variety of shapes.

			If a planar object (or prism, by the [[stretch rule]]) has rotational symmetry such that <math>I_x\,</math> and <math>I_y\,</math> are equal, then the perpendicular axes theorem provides the useful relationship:

			:<math>I_z = 2I_x = 2I_y\,</math>

			== Derivation ==
			Working in Cartesian co-ordinates, the moment of inertia of the planar body about the <math>z\,</math> axis is given by:<ref>{{cite book \|title=Mathematical Methods for Physics and Engineering \|author=K. F. Riley, M. P. Hobson & S. J. Bence \|chapter=Ch. 6: Multiple Integrals \|publisher=Cambridge University Press \|isbn=978-0-521-67971-8 \|year=2006}}</ref>

			:<math>I_{z} = \int \left(x^2 + y^2\right)\, dm = \int x^2\,dm + \int y^2\,dm = I_{y} + I_{x} </math>

			On the plane, <math>z=0\,</math>, so these two terms are the moments of inertia about the <math>x\,</math> and <math>y\,</math> axes respectively, giving the perpendicular axis theorem.
			The converse of this theorem is also derived similarly.

			Note that <math>\int x^2\,dm = I_{y} \ne I_{x} </math> because in <math>\int r^2\,dm </math>, r measures the distance from the ''axis of rotation'', so for a y-axis rotation, deviation distance from the axis of rotation of a point is equal to its x co-ordinate.

			== References ==
			{{reflist}}

			==See also==
			* [[Parallel axis theorem]]
			* [[Stretch rule]]

			{{DEFAULTSORT:Perpendicular Axis Theorem}}
			[[Category:Rigid bodies]]
			[[Category:Physics theorems]]
			[[Category:Articles containing proofs]]
			[[Category:Classical mechanics]]

70.160.254.21: /* Uses */

2012-05-25T20:12:46Z

Uses

New page

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