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			There are several methods for locating the [[center of mass]] of a body.

			== Plumb lines ==
			This method is useful when one wishes to find the [[centroid]] of a complex planar shape with unknown dimensions. It relies on finding the center of mass of a thin body of homogenous [[density]] having the same shape as the complex planar shape.

			{\| border="2" cellspacing="2" cellpadding="2"
			\|-
			\| style="width:32%" \|[[Image:Center gravity 0.svg\|center\|100px]]
			\| style="width:32%" \|[[Image:Center gravity 1.svg\|center\|100px]]
			\| style="width:32%" \|[[Image:Center gravity 2.svg\|center\|100px]]
			\|-
			\| '''Step 1:''' An arbitrary 2D shape.
			\| '''Step 2:''' Suspend the shape from a location near an edge. Drop a [[plumb line]] and mark on the object.
			\| '''Step 3:''' Suspend the shape from another location not too close to the first. Drop a plumb line again and mark. The intersection of the two lines is the center of mass.
			\|}

			==Subdivision==

			=== Of an L-shaped object ===
			This is a method of determining the center of mass of an L-shaped object.

			[[Image:CoG of L shape.svg\|800px\|CG of L-shaped object]]

			#Divide the shape into two rectangles, as shown in fig 2. Find the center of masses of these two rectangles by drawing the diagonals. Draw a line joining the centers of mass. The center of mass of the shape must lie on this line AB.
			#Divide the shape into two other rectangles, as shown in fig 3. Find the centers of mass of these two rectangles by drawing the diagonals. Draw a line joining the centers of mass. The center of mass of the L-shape must lie on this line CD.
			#As the center of mass of the shape must lie along AB and also along CD, it is obvious that it is at the intersection of these two lines, at O. (The point O may or may not lie inside the L-shaped object.)

			=== Of a composite shape ===
			This method is useful when one wishes to find the location of the [[centroid]] or center of mass of an object that is easily divided into elementary shapes, whose centers of mass are easy to find (see ''[[List of centroids]]''). Here the center of mass will only be found in the ''x'' direction. The same procedure may be followed to locate the center of mass in the ''y'' direction.
			{{multiple images
			\|align=center
			\|direction=horizontal
			\|height=200
			\|image1=COG 1.svg
			\|image2=COG 2.svg
			\|image3=COG 3.svg
			}}

			The shape. It is easily divided into a square, triangle, and circle. Note that the circle will have negative area.
			From the [[List of centroids]], we note the coordinates of the individual centroids.
			From equation 1 above:

			<math>\frac{3 \times (-2.5^2\pi) + 5 \times 10^2 + 13.33 \times \frac{10^2}{2}}{ -2.5^2\pi + 10^2 + \frac{10^2}{2}} \approx 8.5 </math> units.

			The center of mass of this figure is at a distance of 8.5 units from the left corner of the figure.

			== Tracing the perimeter ==
			{{Expand section\|date=April 2008}}<!-- Interesting, and just linking to a research paper doesn't do the topic justice. -->
			[[Image:Amsler integrometer front.jpg\|thumb\|left]]
			[[Image:Moment planimeter.jpg\|thumb\|upright=0.75\|right]]
			A direct development of the [[planimeter]] known as an integraph, or integerometer (though a better term is probably moment planimeter), can be used to establish the position of the [[centroid]] or center of mass of an irregular shape. This method can be applied to a shape with an irregular, smooth or complex boundary where other methods are too difficult. It was regularly used by ship builders to ensure the ship would not capsize. See [http://web.mat.bham.ac.uk/C.J.Sangwin/Publications/integrometer.pdf Locating the center of mass by mechanical means].

			==References==
			{{Reflist}}

			[[Category:Statics]]
			[[Category:Geometric centers]]

en>DinosaursLoveExistence: /* See also */ de:Hydroxylzahl

2012-06-17T13:17:06Z

See also: de:Hydroxylzahl

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Hydroxyl value - Revision history

en>Cweisbecker at 04:36, 29 December 2013

en>DinosaursLoveExistence: /* See also */ de:Hydroxylzahl