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CENTROIDS

 

Centroid Of An Area

 

 

The centroid of an area is similar to the center of mass of a body. Calculating the centroid involves only the geometrical shape of the area. The center of gravity will equal the centroid if the body is homogenous i.e. constant density. Integration formulas for calculating the Centroid are:

 

 

When calculating the centroid of a complex shape. Divide the shape up into a combination of known shapes. Then use the the following formula:

 

 

The distance from the y-axis to the centroid is Cx
The distance from the x-axis to the centroid is Cy
The coordinates of the centroid are (Cx , Cy)

 

 

The centroid location of many common shapes is known. The Properties of Areas page includes the Centroid Location, Area, Area Moments of Inertia, Area Polar Moments of Inertia, & Area Radius of Gyration for many common shapes.

 

Center of Mass

 

The Center of Mass (center of gravity) of a solid is similar to the Centroid of Solid. However, calculating the centroid involves only the geometrical shape of the solid.

The center of gravity will equal to the centroid if the body is homogenous i.e. constant density.

Integration formulas for calculating the Center of Mass are:

 

 

The perpendicular distance in the x direction from the yz-plane to the Center of Mass is Cx
The perpendicular distance in the y direction from the zx-planeto the Center of Mass is Cy
The perpendicular distance in the z direction from the xy-plane to the Center of Mass is Cz
The coordinates of the Center of Mass are (Cx , Cy , Cz).

 

 

 

 

Composite Solids

 

When calculating the centroid of a complex shape. Divide the shape up into a combination of known shapes. Then use the the following formula:

 

 

The perpendicular distance in the x direction from the ys-plane to the Center of Mass is Cx
The perpendicular distance in the y direction from the zx-plane to the Center of Mass is Cy
The perpendicular distance in the z direction from the xy-plane to the Center of Mass is Cz
The coordinates of the Center of Mass are (Cx , Cy , Cz)

Centroid of Solids

 

The centroid of a solid is similar to the center of mass. However, calculating the centroid involves only the geometrical shape of the solid.

The center of gravity will equal the centroid if the body is homogenous i.e. constant density.

Integration formulas for calculating the Centroid are:

 

 

The perpendicular distance in the x direction from the yz-plane to the centroid is Cx
The perpendicular distance in the y direction from the zx-plane to the centroid is Cy
The perpendicular distance in the z direction from the xy-plane to the centroid is Cz
The coordinates of the centroid are (Cx , Cy , Cz).