ECS221L15

# ECS221L15 - Centroids by Integration Recall xA = x dA y A =...

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Centroids by Integration Recall: = = B B dA y A y dA x A x dx dy rd θ dr

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Reduction to Single Integral     Element area: dA = ydx Element centroid: x el = x y el = y/2 = = = B b a el B xy(x)dx ydx x dA x A x = = = B b a el B y(x)dx 2 y(x) ydx y dA y A y y x x el y el y dx x
Another way …              Element area: dA = (a-x)dy Element centroid: x el = x+(a-x)/2 y el = y - = - = = - = - = = B el B B 2 2 el B x(y))dy y(a x(y))dy (a y dA y A y dy 2 x(y) a x(y))dy (a x dA x A x y x x y dy a

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Polar Coordinates Element area: dA=r 2 d θ /2 Element centroid: r el =2r/3 =

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ECS221L15 - Centroids by Integration Recall xA = x dA y A =...

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