Center of Gravity

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Center of Gravity Centroid
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To replace the system of particles / bodies by a
simple system composed of only one body , tow
conditions must be satisfied (( as far as Statics
is concerned )). Thus the tow system will be
equivalent.
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Forces in the two systems must be
equal. Fy W wi
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Moments in the two systems must be equal. Mx
Z W zi wi Z
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Similarly Mz X
If wi gets smaller and smaller , then wi
wi dwi W ( w)i
W ?dw Similarly, X
y .. , Z .
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Centroid For Particles X wi xi
wi X Y
Z
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Center of Gravity for bodies X
Y . Z ..
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Center of Mass X Y
. Z .
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Centroid X , y .. , Z
.. V X
. A X
..
L
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X A ? x d A y A ? y d A
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?x d A first moment of the are with respect
to the y-axis ? y d A
x- If
the centroid of an area is located on a
coordinate axis, then the first moment of the
area wrt that axis is ZERO. We can go the other
way If .
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Symmetry Take Advantage of
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Centroid for Composite Bodies Volumes areas
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We can come back to the original definition. Use
instead of ?.
...
X Xi Vi / Vi . . . . . . .
X Xi Ai / Ai . . . . . . .
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