Centroids; Centers of Gravity

1
Centroids Centers of Gravity

• How do you know where to locate the resultant
  weight of a body?

2
Center of Gravity of a Planar Body

• Assume body is composed of small elements such
  that all element weight vectors are parallel.

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• Resultant weight W?W1?W2?Wn
• Find location by moment balance.

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• The quantities locate the center of
  gravity of the planar body B.

5
Centroids of Areas

• Areas. ?W gt?A , W gtA

6
Centroids of Lines

• Lines. ?W gA?L , W gAL

7
First Moments Symmetry

• First moments Qx ?ydA Qy ?xdA
• An area is symmetric with respect to an axis if
  there is a line joining every 2 points which is
  perpendicular to the axis and bisected by it.

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• For areas with 2 axes of symmetry the centroid is
  at the intersection of the axes.
• An area has a center of symmetry if element at
  (x,y) has mirror image (-x,-y).

9
Composite Areas

• Compute the centroids of areas composed of simple
  shapes.