Mathematics-Online lexicon: Mass, Center of Mass, Barycenter

	[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]
	Mathematics-Online lexicon:
	Mass, Center of Mass, Barycenter

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The mass of a solid

with density $\varrho(x),\,x\in K$ is

$\displaystyle m = \int\limits_K \varrho(x)\,dK$

The $\nu$ - th coordinate of the center of mass is

$\displaystyle s_\nu = m^{-1}\int\limits_K x_\nu\varrho(x)\,dK \ .$

In the special case when $\varrho(x) = 1$ the first integral yields the volume of The $\nu$ - th coordinate of the (geometric) barycenter of is

$\displaystyle s_\nu = V^{-1}\int\limits_K x_\nu \,dK \ .$

()

Examples:

automatically generated 8/ 4/2008