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Centroids by Integration

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Centroids by Integration. Recall: dx. dy. rdq. dr. Reduction to ... of Pappus and ... A solid of revolution is a formed by rotating a plane area about an ... – PowerPoint PPT presentation

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Title: Centroids by Integration


1
Centroids by Integration
  • Recall

2
Reduction to Single Integral
  • Element area dA ydx
  • Element centroid
  • xel x yel y/2

3
Another way
  • Element area dA (a-x)dy
  • Element centroid
  • xel x(a-x)/2 yel y

4
Polar Coordinates
  • Element area dAr2dq/2
  • Element centroid rel2r/3

5
Theorems of Pappus and Guldinus
  • A surface of revolution is a formed by rotating a
    plane curve about an axis.

6
more
  • A solid of revolution is a formed by rotating a
    plane area about an axis.

7
Theorem 1
  • A 2p L

8
Theorem 2
  • V 2p A
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