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) |

Figure | |

Parabolic Segment | |

Semicircle |

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

(4) |

(5) |

(6) |

(7) |

**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

1999-05-26