ES-180 Center of Gravity and Centroids by Integration |
where x_{el} - x-coordinate of CG of element dW y_{el} - y-coordinate of CG of element dW and the centroid | If a body is not composed of standard sections, but its area is integrable, the method of integration may be used to find the CG. |
where
x_{el} = x y_{el} = y/2 dA = y dx |
The location and calculation for a vertical element are shown here...
Note: the centroid of a rectangle is in its center. |
where y_{el} = y dA = (a-x) dy | For a horizontal element, the location and calculations are shown... |
where | If the centroid or CG is desired in polar coordinate for ease of integration the diagram and calculations are shown here...> |
| Note: The differential area of the sector is a triangular element... |
and the CG of a triangle is one third of the altitude from the base or two thirds the altitude from the apex. |