en>Yobot: WP:CHECKWIKI error fixes using AWB (10093)

2014-05-05T09:35:09Z

WP:CHECKWIKI error fixes using AWB (10093)

en>Xnn: remove opinion

2013-03-12T16:07:17Z

remove opinion

← Older revision		Revision as of 18:07, 12 March 2013
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	~~Alyson~~ is ~~what my spouse enjoys~~ to ~~contact me but I don~~'t ~~like when individuals use my full title~~. ~~My wife~~ and ~~I live in Mississippi~~ and ~~I adore each day residing here~~. ~~My working day occupation~~ is ~~are psychics real~~ ([http://~~galab-work~~.cs.~~pusan~~.ac.kr/~~Sol09B~~/~~?document_srl~~=~~1489804 galab~~-~~work~~.cs.~~pusan~~.ac.kr]) a ~~journey agent~~. ~~I am truly fond~~ of ~~to go to karaoke but I~~'~~ve been taking on new things lately~~.<br><br>~~Also visit my~~ web~~-site :: telephone [https~~://www.~~machlitim~~.~~org~~.il/~~subdomain~~/~~megila~~/~~end~~/~~node~~/~~12300 psychic phone~~] ([http://www.~~aseandate~~.com/~~index~~.~~php?m~~=~~member_profile&p~~=~~profile&id~~=~~13352970 Privacy~~ of ~~Data:~~ This ~~tool~~ is ~~built~~-with and ~~functions~~-~~in Client Side JavaScripting~~, ~~so only your computer will see or process your data input~~/~~output~~.~~a cool way to improve~~])		The following is a list of [[second moment of area\|area moments of inertia]]. The area moment of inertia or [[second moment of area]] has a [[physical unit\|unit]] of dimension length<sup>4</sup>, 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==

			{\|class="wikitable"
			\|-
			! Description \|\| Figure \|\| Area moment of inertia \|\| Comment \|\| Reference
			\|-
			\| a filled circular area of radius ''r''\|\|[[Image:Area moment of inertia of a circle.svg]]\|\|<math>I_0 = \frac{\pi}{4} r^4</math>\|\| \|\|<ref>{{cite web\|url=http://www.efunda.com/math/areas/Circle.cfm\|title=Circle\|accessdate=2006-12-30\|publisher=eFunda}}</ref>
			\|-
			\| an [[annulus (mathematics)\|annulus]] of inner radius''r''<sub>1</sub> and outer radius''r''<sub>2</sub>\|\|[[Image:Area moment of inertia of a circular area.svg]]\|\|<math>I_0 = \frac{\pi}{4} \left({r_2}^4-{r_1}^4\right)</math>\|\| For thin tubes, this is approximately equal to: <math>\pi \left(\frac{{r_2}+{r_1}}{2}\right)^3 \left({r_2}-{r_1}\right)</math> or <math>\pi {r}^3{t}</math> .\|\|
			\|-
			\| a filled [[circular sector]] of angle ''θ'' in [[radian]]s and radius ''r'' with respect to an axis through the centroid of the sector and the center of the circle\|\|[[Image:Area moment of inertia of a circular sector.svg]]\|\|<math>I_0 = \left( \theta -\sin \theta \right) \frac{r^{4}}{8}</math>\|\|This formula is valid for only for 0 ≤ <math>\theta</math> ≤ <math>\pi</math> \|\|
			\|-
			\| a filled semicircle with radius ''r'' with respect to a horizontal line passing through the centroid of the area\|\|[[Image:Area moment of inertia of a semicircle 2.svg]]\|\|<math>I_0 = \left(\frac{\pi}{8} - \frac{8}{9\pi}\right)r^4 \approx 0.1098r^4 </math>\|\| \|\|<ref name=semicircle>{{cite web\|url=http://www.efunda.com/math/areas/CircleHalf.cfm\|title=Circular Half\|accessdate=2006-12-30\|publisher=eFunda}}</ref>
			\|-
			\| a filled semicircle as above but with respect to an axis collinear with the base\|\|[[Image:Area moment of inertia of a semicircle.svg]]\|\|<math>I = \frac{\pi r^4}{8}</math>\|\|This is a consequence of the [[parallel axis theorem]] and the fact that the distance between these two axes is <math>\frac{4r}{3\pi}</math>\|\|<ref name=semicircle />
			\|-
			\| a filled semicircle as above but with respect to a vertical axis through the centroid\|\|<center>[[Image:Area moment of inertia of a semicircle 3.svg]]</center>\|\|<math>I_0 = \frac{\pi r^4}{8}</math>\|\| \|\|<ref name=semicircle />
			\|-
			\| a filled quarter circle with radius ''r'' entirely in the 1st quadrant of the [[Cartesian coordinate system]]\|\|[[Image:Area moment of inertia of a quartercircle.svg]]\|\|<math>I = \frac{\pi r^4}{16}</math>\|\| \|\|<ref name=quartercircle>{{cite web\|url=http://www.efunda.com/math/areas/CircleQuarter.cfm\|title=Quarter Circle\|accessdate=2006-12-30\|publisher=eFunda}}</ref>
			\|-
			\| a filled quarter circle as above but with respect to a horizontal or vertical axis through the centroid\|\|[[Image:Area moment of inertia of a quartercircle 2.svg]]\|\|<math>I_0 = \left(\frac{\pi}{16}-\frac{4}{9\pi}\right)r^4</math>\|\|This is a consequence of the [[parallel axis theorem]] and the fact that the distance between these two axes is <math>\frac{4r}{3\pi}</math> \|\|<ref name=quartercircle />
			\|-
			\| a filled [[ellipse]] whose radius along the ''x''-axis is ''a'' and whose radius along the ''y''-axis is ''b''\|\|[[Image:Area moment of inertia of an ellipsis.svg]]</td><td><math>I_0 = \frac{\pi}{4} ab^3</math>\|\| \|\|
			\|-
			\| a filled rectangular area with a base width of ''b'' and height ''h''\|\|[[Image:Area moment of inertia of a rectangle.svg]]\|\|<math>I_0 = \frac{bh^3}{12}</math>\|\| \|\|<ref name=rect>{{cite web\|url=http://www.efunda.com/math/areas/rectangle.cfm\|title=Rectangular area\|accessdate=2006-12-30\|publisher=eFunda}}</ref>
			\|-
			\| a filled rectangular area as above but with respect to an axis collinear with the base\|\|[[Image:Area moment of inertia of a rectangle 2.svg]]\|\|<math>I = \frac{bh^3}{3}</math>\|\|This is a result from the [[parallel axis theorem]]\|\|<ref name=rect />
			\|-
			\| 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\|\| \|\|<math>I = \frac{bh^3}{12}+bhr^2</math>\|\|This is a result from the [[parallel axis theorem]]\|\|<ref name=rect />
			\|-
			\| a filled triangular area with a base width of ''b'' and height ''h'' with respect to an axis through the centroid\|\|[[Image:Area moment of inertia of a triangle.svg]]\|\|<math>I_0 = \frac{bh^3}{36}</math>\|\| \|\|<ref name=tri>{{cite web\|url=http://www.efunda.com/math/areas/triangle.cfm\|title=Triangular area\|accessdate=2006-12-30\|publisher=eFunda}}</ref>
			\|-
			\| a filled triangular area as above but with respect to an axis collinear with the base\|\|[[Image:Area moment of inertia of a triangle 2.svg]]\|\|<math>I = \frac{bh^3}{12}</math>\|\|This is a consequence of the [[parallel axis theorem]] \|\|<ref name=tri />
			\|-
			\| a filled [[regular hexagon]] with a side length of ''a''\|\|[[Image:Area moment of inertia of a regular hexagon.svg]]\|\|<math>I_0 = \frac{5\sqrt{3}}{16}a^4</math>\|\|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.\|\|
			\|
			\|-
			\| Any plane region with a known area moment of inertia for a parallel axis. (Main Article [[parallel axis theorem]]) \|\|[[Image:Parallel Axes Compact.png]]\|\|<math>I_z = I_x + Ar^2</math> \|\| 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.
			\|}

			==See also==

			* [[List of moments of inertia]]

			==References==
			{{reflist}}

			==External links==
			* [http://www.amesweb.info/SectionalPropertiesTabs/SectionalProperties.aspx Online Sectional Properties Calculator]
			* [http://civilengineer.webinfolist.com/str/micalc.htm Online Calculator for Area Moment of Inertia ]
			[[Category:Mechanics\|Area moment of inertia]]
			[[Category:Physics-related lists\|Area moments of inertia]]

en>Brad7777: /* References */ removed catgeory mathematical analysis

2011-11-20T17:29:19Z

References: removed catgeory mathematical analysis

New page

Alyson is what my spouse enjoys to contact me but I don't like when individuals use my full title. My wife and I live in Mississippi and I adore each day residing here. My working day occupation is are psychics real ([http://galab-work.cs.pusan.ac.kr/Sol09B/?document_srl=1489804 galab-work.cs.pusan.ac.kr]) a journey agent. I am truly fond of to go to karaoke but I've been taking on new things lately.<br><br>Also visit my web-site :: telephone [https://www.machlitim.org.il/subdomain/megila/end/node/12300 psychic phone] ([http://www.aseandate.com/index.php?m=member_profile&p=profile&id=13352970 Privacy of Data: This tool is built-with and functions-in Client Side JavaScripting, so only your computer will see or process your data input/output.a cool way to improve])

Convergence problem - Revision history

en>Yobot: WP:CHECKWIKI error fixes using AWB (10093)

en>Xnn: remove opinion

en>Brad7777: /* References */ removed catgeory mathematical analysis