Centre of Gravity and Centroids

[DiamondV]

Homework Statement

http://puu.sh/lJgzB/5b877de108.jpg

http://puu.sh/lJgAR/c28393f051.jpg

Can someone please explain these two slides to me? Especially the first one, It seems to be summing the Moments in y and Moments in x. The sum of the moments in y is xW. I understand that but then it says that xW is equal to Sum of X times Change in W. Thats what I don't get. This is like the first page of the notes, there's no other info given. This is all.
EDIT: I've realized that we are assuming that the rigid body is made up of millions of tiny particles each at different distances(x) and different weights(W). So we sum it. But I still don't get why we use Delta W instead of W itself?

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Homework Statement

http://puu.sh/lJgzB/5b877de108.jpg

http://puu.sh/lJgAR/c28393f051.jpg

Can someone please explain these two slides to me? Especially the first one, It seems to be summing the Moments in y and Moments in x. The sum of the moments in y is xW. I understand that but then it says that xW is equal to Sum of X times Change in W. Thats what I don't get. This is like the first page of the notes, there's no other info given. This is all.
EDIT: I've realized that we are assuming that the rigid body is made up of millions of tiny particles each at different distances(x) and different weights(W). So we sum it. But I still don't get why we use Delta W instead of W itself?

Because W is the weight of the entire plate or piece of wire.

 

[DiamondV]

Because W is the weight of the entire plate or piece of wire.

Why is Change in W used then?(delta W)

 

[DiamondV]

Or is the Delta W just signifying the weight of the individual tiny particle that when summed together(sigma) results in the weight of the the rigid body?

 

[SteamKing]

Or is the Delta W just signifying the weight of the individual tiny particle that when summed together(sigma) results in the weight of the the rigid body?

Right. $W = \int dW$