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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).
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 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).

The centroid location of many common shapes can be found through the Properties of Solids page which also includes Volume, Mass Moments of Inertia, Mass Polar Moments of Inertia, and Mass Radius of Gyration.