Center of Gravity Centroid

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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 fas as Statics
is conserned )). Thus the tow system will be
equivalent.
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Fours in the two systems must be
equed. Fy W wi
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Moments in the two system munt be equal. Mx
Z W Zi wi Z
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Similarly mz X
If wi guts smlle and sudlue , than wi
wi dwi W ( w)i
W ?dw similarly, X y . ,
Z.
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C. For Petals Centroid X wi
Xi wi X Y
Z
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C.G. for bodies X Y
. Z ..
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C.M. X Y .
Z . .
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Centeraid 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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?xd A frist moment of the are wrt 202 is ?
y d A
X- If the centrid of an are is located on a
coodinet axis ,then the first moment of the are
wrt that axin is ZERO
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Symmery Talce Advantaye at
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Centroid for Composite Bodies Volumes anas
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We can come back to the origiud definitin. Use
instead of ?.
...
X Xi Vi / Vi . . . . . . .
X Xi Ai / Ai . . . . . . .
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