Centroids and Centers of Gravity

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Centroids of Composite Figures

Center of gravity of a homogeneous flat plate
$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$


Centroids of areas
$A \, \bar{x} = \Sigma ax$

$A \, \bar{y} = \Sigma ay$


Centroids of lines
$L \, \bar{x} = \Sigma lx$

$L \, \bar{y} = \Sigma ly$


Center of Gravity of Bodies and Centroids of Volumes

Center of gravity of bodies
$W \, \bar{x} = \Sigma wx$

$W \, \bar{y} = \Sigma wy$

$W \, \bar{z} = \Sigma wz$


Centroids of volumes
$V \, \bar{x} = \Sigma vx$

$V \, \bar{y} = \Sigma vy$

$V \, \bar{z} = \Sigma vz$


Infinite Series

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Sequences and Series

Sequence is a succession of numbers formed according to some fixed rule. Example is

$1,~ 8,~ 27,~ 64,~ 125,~ ...$

which is a sequence so that the nth term is given by n3.

Series is the indicated sum of a sequence of numbers. Thus,

$a_1 + a_2 + a_3 + ... + a_n + ...$

is the series corresponding to the sequence $a_1,~ a_2,~ a_3,~ ... ,~a_n,~ ...$

Finite and Infinite Series