Mechanics: Statics Distributed Force 2D Plane Body Centroid of Plane Body by Integration Draft for Information Only
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Centroid of 2D
Plane Body
Centroid of 2D Plane BodyThe centroid of an plate is determined by the first moment of a two dimensional plane body with the method of the first moment of area. And the centroid of a wire is determined by the first moment of a two dimensional plane body with the method of the first moment of line. Centroids of AreasArea by IntegrationArea by Double IntegrationFor example, the signed area of the planar region R is bounded by curves in rectangular form , Imply An elemental area ΔA in rectangular form can be defined as Δx times Δy. Imply In general, the area of a region can be determined by multiple integration through sweeping the signed elemental area starting from along either rectangular coordinate axis. Imply Starting from horizontal sweeping along x axis Starting from vertical sweeping along y axis And for curves in polar form For example, the signed area of the planar region R is bounded by curves in polar form , For the curve profile, Imply And the curve profile in terms of θ, imply And other boundary curves are An elemental area ΔA in polar form can be approximated by Δr times rΔθ. Imply Unlike rectangular form, the polar form of an elemental area ΔA is not a constant but a function of r and in turn a function of θ also. In general, the area of a region can be determined by multiple integration through sweeping the signed elemental area starting from along either polar variables. Imply Starting from radical sweeping along variable radius r Starting from circular sweeping along variable angle θ, ©sideway ID: 120500016 Last Updated: 2/6/2012 Revision: 1 Ref: References
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