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Definition of Centroid - Centroid and Centre of Gravity - Engineering Mechanics

let us take the new chapter in mechanics

the name of the chapter is centroid and

centre of gravity here we have the first

part as centroid and the second part of

the chapter is centre of gravity

first let us understand what is centroid

here I will be writing the definition of

centroid centroid it is a single point

about which entire area is acting for a

lamina or plain figure irrespective of

the position

of the plane figure

so here I have written the definition of

centroid by centroid we mean that it is

a single point about which entire area

is acting for a lamina or plane figure

irrespective of the position of plane

figure so from the definition it is

understood that centroid is applicable

only for plane figures and when I talk

about plane figures plane figures means

only two de figures no three de figures will be

here so here I can see that it is

applicable to plane figures having area

but no volume so here I have clearly

defined what is centroid when you talk

about centroid it means you are talking

about a figure which has area but which

has no volume so by no volume it is

clear that it is not a solid but a two de

figure examples some of the two de figures

are rectangle square circle semi circle

triangle quarter circle etc so here I

have given some of the examples of plane

figures it means whenever we will

calculate the centroid we will be

calculating the centroid only for these

figures or if it is possible you can

combine like for example you can combine

rectangle and semi circle then it

becomes a composite figure that is

called as a composite figure composite

figure is that figure in which you are

having more than one plane figure so if

you have two plane figures it becomes a

composite plane figure and it you can

even go on increasing the number of

plane figures minimum two are required

so come this here it is very much clear

about the centroid the definition part

that it was it was a single point about

which the entire area is acting for a

lamina or plane figure irrespective of

the position irrespective of the

position means even if you go on

changing the orientation like for

example if there is a triangle we are

having the apex at the top even if the

apex is at the bottom then at that time

also the centroid will not change it is

a point which remains constant now let

me draw a diagram which will indicate

which will explain you the concept of

centroid let me consider a plane figure

which is of any general shape now this

figure which I have it consists of small

small areas here there will be area one

for example area ttwo area three and so on

so this figure is made up of small small

areas here I have denoted them and like

this you have number of areas which are

acting over this plain figure now these

small small areas will give us the total

area which is denoted by capital A now

instead of having individual areas if I

want to denote the total area at that

single point that single point would be

called as the centroid so here if I draw

this figure again instead of showing

individual areas I will be showing the

total area by one particular point and

that point becomes centroid centroid is

denoted by letter G and the location of

the centroid with respect to y-axis it

is X bar and the location of centroid

with respect to y axis with respect to y

it was X bar with respect to x-axis the

distance of the centroid is y bar so in

other words here we have a single point

which is denoting the entire area

instead of showing area on individual

points we can show area on one single

point and that single point is nothing

but the centroid so here the letter G

which I have written this indicates the

centroid so it is very much clear from

this concept of centroid that if we want

to locate the centroid it would be

located by finding the values of x bar

and y bar X bar Y bar are the

coordinates which gave us the centroid

and

in this chapter we will just locate the

centroid so with this I think the

definition part and the concept it might

be understood to you all