Lecture 22 - location of the centroid Centroids& Center...

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12/4/10 Centroids & Center of Mass/Gravity Centroid – The geometric center of an object. 2L/3 x x y y
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12/4/10 Centroids & Center of Mass/Gravity x y L x 3 2 = L y 3 1 = In general… Centroid only depends on geometry, not density
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12/4/10 Coordinates of the centroid , or average position, of an area is… = = A A A A dA ydA y dA xdA x 2 x y y = x2 –x + 1 Determine the x-component of the centroid of the area.
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12/4/10 In discrete form, or when dealing with a combination of simple shapes… = = A A A A dA ydA y dA xdA x = = i i i i i i i i i i A A y y A A x x Sum of individual centroids times area Sum of areas Centroids of Composite Areas 1 2 x y
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12/4/10 12’ 6” 4” 15” 6” 4” 18” 24” ? ? = = x y
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12/4/10 3” 4” 4” 1” Find the
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Unformatted text preview: location of the centroid. 12/4/10 Centroids & Center of Mass/Gravity Center of gravity vs. Center of mass The point at which the resultant weight of a system of particles acts. Since c.g. depends on the acceleration of gravity, center of mass is a better term to use. Center of gravity of the solar system??? Center of mass is independent of gravity. 12/4/10 c.g. ∑ ∑ ∑ ∑ ∑ ∑ = = = W zW z W yW y W xW x Center of mass ∑ ∑ ∑ ∑ ∑ ∑ = = = m zm z m ym y m xm x 100 lb 300 lb 100 lb (4,8)f t (10,6)f t (5,3)f t Find the center of gravity....
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