Lesson 18 - Centroid of Volume

Lesson 18 - Centroid of Volume - TOPIC APPLICATIONS...

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TOPIC APPLICATIONS CENTRIODS OF SOLIDS OF REVOLUTION

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Center of gravity of a solid of revolution The coordinates of the centre of gravity of a solid of revolution are obtained by taking the moment of an elementary disc about the coordinate axis and then summing over all such discs. Each sum is then approximately equal to the moment of the total volume taken as acting at the centre of gravity. Again, as the disc thickness approaches zero the sums become integrals: 2 2 and 0 b x a b x a xy dx x y y dx = = = =
of volume V, generated by revolving a plane area about a horizontal or vertical axis, with respect to the plane through the origin and perpendicular to the axis may be found as follows: 1.Sketch the region, showing a representative strip and the approximating rectangle. 2.Form the product of the volume, disc or shell generated by revolving the rectangle about the axis and the distance of the centroid of the rectangle from the plane, and sum for all the rectangles. 3.Assume the number of rectangles to be indefinitely increased

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Lesson 18 - Centroid of Volume - TOPIC APPLICATIONS...

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