Centroid, Center of Gravity and Moment of Inertia

Centroid 

Centroid of an area lies on the axis of symmetry if it exists.

 xc =  Σ Ai xi 

 yc =  Σ  Ai yi

xc = (A1. x 1 + A1. y1) ÷ (A1 + A2 )

   yc = (A1 y1 + A2 y2 ) ÷ (A1 + A2)  

xc = yc =  (Moment of area) ÷ (Total area)

xc = Σ x.dA  

              A

yc = Σ y.dA   

                         A

Derivations For finding the Centroid of different Regular Areas

Centre of gravity

Centre of gravity: 

It is that point through which the resultant of the distributed gravity force passes regardless of the orientation of the body in space.

As the point through which the resultant of the force of gravity (weight) of the body acts.

Centre of gravity is applied to bodies with mass and weight, While centroid is applied to plane areas.

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