Centroids and Centers of Gravity

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Centroids of Composite Figures

Center of gravity of a homogeneous flat plate
Wˉx=Σwx

Wˉy=Σwy

 

Centroids of areas
Aˉx=Σax

Aˉy=Σay

 

Centroids of lines
Lˉx=Σlx

Lˉy=Σly

 

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Center of Gravity of Bodies and Centroids of Volumes

Center of gravity of bodies
Wˉx=Σwx

Wˉy=Σwy

Wˉz=Σwz

 

Centroids of volumes
Vˉx=Σvx

Vˉy=Σvy

Vˉz=Σvz

 

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Infinite Series

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,

a1+a2+a3+...+an+...

is the series corresponding to the sequence a1, a2, a3, ..., an, ...
 

Finite and Infinite Series