Centroid of 2D Plane Body

The centroid of an plate is determined by the first moment of a two dimensional plane body with the method of the first moment of area.

And the centroid of a wire is determined by the first moment of a two dimensional plane body with the method of the first moment of line.

Centroids of Shapes

1. Centroid of Quarter-Circular Area

   Area of Quarter-Circular: http://output.to/sideway/default.asp?qno=111100013

   

   Coordinate x of centroid by integration.

   

   Coordinate x of centroid

   

   Similarly, coordinate y of centroid by integration.

   
2. Centroid of Semi-Circular Area

   Area of Semi-Circular: http://output.to/sideway/default.asp?qno=111100013

   

   Coordinate x of centroid by symmetry.

   

   Coordinate y of centroid by integration.

   
3. Centroid of Quarter-Elliptical Area

   Area of Quarter-Elliptical: http://output.to/sideway/default.asp?qno=111100013

   

   Coordinate x of centroid by integration.

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.

   
4. Centroid of Semi-Elliptical Area

   Area of Semi-Elliptical: http://output.to/sideway/default.asp?qno=111100013

   

   Coordinate x of centroid by symmetry.

   

   Coordinate y of centroid by integration.

   
5. Centroid of Quarter-Parabolic Area

   Area of Quarter-Parabolic:

   

   Coordinate x of centroid by integration.

   

   Coordinate x of centroid by integration.

   

   Similarly, coordinate y of centroid by integration.

   
6. Centroid of Quarter-Parabolic Area

   Area of Quarter-Parabolic:

   

   Coordinate x of centroid by symmetry.

   

   Similarly, coordinate y of centroid by integration.