T03.2 CoG & Centroid

T03.2 CoG & Centroid - Center of Gravity (CoG) &...

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Center of Gravity (CoG) & Centroid T03.2
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CoG: System of Particles x y z W i x y z W R CoG i x i z i y x z y 12 y n R F W W W W  g 1 1 2 2 x n n R M W z W z W z W z 1 1 2 2 z n n R M W x W x W x W x 1 1 2 2 z n n R M Wy W y W y W y y x z ii i xW x W i yW y W i zW z W
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CoG: Continuous Body x y z dW dV xdW x dV x dW dV   ydW y dV y dW dV zdW z dV z dW dV
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Centroid Geometric center xdV x dV ydV y dV zdV z dV NOTE: If the body density is homogeneous (i.e., does not vary spatially) then CoG = centroid.
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Example x y a Find the centroid.
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Hibbeler’s Appendix C
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Composite Bodies x y z ii i xW x W i yW y W i zW z W i xV x V i yV y V i zV z V CoG Centroid NOTE: App. C will be useful. i xA x A i yA y A i zA z A 3D 2D
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Example x y Find the centroid. 2” 4” 2” 2” 6”
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Example—Revisited x y a Find the centroid, using composite bodies. 3 3 00 2 2 0 0 1 1 () 2 3 3 1 3 1 2 2 a a aa mx ma x mxdx xdA xa dA mxdx ma mx
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This note was uploaded on 12/19/2010 for the course EGR 75 taught by Professor Virgin during the Fall '08 term at Duke.

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T03.2 CoG & Centroid - Center of Gravity (CoG) &...

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