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Published byOpal Daniels Modified over 9 years ago
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Centers of Mass
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Particles of masses 6, 1, 3 are located at (-2,5), (3,3) & (3,-4) respectively. Find
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Find the centroid (center of mass with uniform density) of the region shown, by locating the centers of the rectangles and treating them as point masses…..
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We can extend this idea to the more general continuous case, where we are finding the center of mass of a region of uniform density bounded by 2 functions….. We can find the area by slicing:
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We can extend this idea to the more general continuous case, where we are finding the center of mass of a region of uniform density bounded by 2 functions….. We find the Moments, by locating the centers of the rectangles and treating them as point masses….. This slice has balance point at:
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Center of Mass: 2-Dimensional Case The System’s Center of Mass is defined to be:
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Find the center of mass of the thin plate of constant density formed by the region y = 1/x, y = 0, x =1 and x=2. Each slice has balance point:
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Find the center of mass of the thin plate of constant density formed by the region y = cos(x) and the x-axis Each slice has balance point:
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Find the center of mass of the the lamina R with density 1/4 in the region in the xy plane bounded by y = 3/x and y = 7 - 4x. Each slice has balance point: Bounds:
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Find the center of mass of the the lamina R with density 1/2 in the region in the xy plane bounded by y = 6x -1 and y = 5x 2. Use slices perpendicular to the y-axis. Each slice has balance point: Bounds:
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