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ECS221L16

# ECS221L16 - Composite Bodies Compute the centroids of...

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Centroids, Centers of Gravity for 3-D Bodies Locate position vector defining center of gravity. r r -Wj - Wj G

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Procedure Divide body into small elements. Equate force and moment sums to resultants. = - × = × = - = rdW W r ) j ΔW ( r ) j (-W r dW W j ΔW j W - = = dW r W r dW W = = dV r V r dV V Uniform body:
Component Form Recall: k z j y i x r k z j y i x r + + = + + = , = = = zdW W z ydW W y xdW W x = = = zdV V z ydV V y xdV V x zdV , ydV , xdV 1 st moments: yz, xz, xy plane Uniform

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Symmetry How many planes of symmetry?

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Unformatted text preview: Composite Bodies Compute the centroids of volumes composed of simple shapes. i n 1 i i i n 1 i i i n 1 i i n 1 i i V z V z V y V y V x V x V V ∑ ∑ ∑ ∑ = = = = = = = = Centroids by Integration Bodies with 2 planes of symmetry: x y z dV = π r 2 (x) dx x el =x z y = = ∫ = dV x V x el...
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ECS221L16 - Composite Bodies Compute the centroids of...

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