## Centroid (Geometric)

The Center of Mass of a 2-D planar Lamina or a 3-D solid. The mass of a Lamina with surface density function is

 (1)

The coordinates of the centroid (also called the Center of Gravity) are

 (2)

 (3)

The centroids of several common laminas along the nonsymmetrical axis are summarized in the following table.

 Figure Parabolic Segment Semicircle

In 3-D, the mass of a solid with density function is

 (4)

and the coordinates of the center of mass are
 (5)

 (6)

 (7)

 Figure Cone Conical Frustum Hemisphere Paraboloid Pyramid

See also Pappus's Centroid Theorem

References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 132, 1987.

McLean, W. G. and Nelson, E. W. First Moments and Centroids.'' Ch. 9 in Schaum's Outline of Theory and Problems of Engineering Mechanics: Statics and Dynamics, 4th ed. New York: McGraw-Hill, pp. 134-162, 1988.

© 1996-9 Eric W. Weisstein
1999-05-26