# Center Of Mass Deriving

1. Apr 20, 2009

### Dweirdo

OMG second time I'm opening a thread in the wrong forum FFS!!!!
Damn bookmarks!! MODS move it please.
1. The problem statement, all variables and given/known data
Not a home work question, just something i cam across and need a clarification.
Could One show me how to derive to the equation that X(cm)=int(X dm)/M
int=the deformed S of the integral(2 lazy to write in Latex XD).

2. Relevant equations
X(cm)=sigma(Xi Dmi)/M

3. The attempt at a solution
I know It's simple, But I can't imagine how sigma(Xi Dmi) becomes int(X dm),
I don't understand what it means , trying to convert it to words just doesn't work for me,so could some 1 explain that for me?
AFAIK sigma(Xi Dmi) means the mass distribution,but how does the integral takes place here?
I really need to understand the math part in physics.

Thanks a lot in advanced !

Last edited: Apr 20, 2009
2. Apr 20, 2009

### tiny-tim

Hi Dweirdo!

(have a sigma: ∑ and a delta: ∆ and an integral: ∫ and try using the X2 tag just above the Reply box )
How does ∑ Xi ∆mi become ∫ X dm ?

Because that's what an ∫ is …

it's defined as the limit of a ∑ as the ∆s tend to zero.

3. Apr 21, 2009

### Dweirdo

But why?? Like I know that in Energy, if you make a graph of force and distance and it is curved than integral calculates the plot.
but wtf is it here?
thanks :}

4. Apr 21, 2009

### tiny-tim

Because energy (= work done ) = force x distance, so it's the limit of ∑ (force x ∆distance)

Similarly, moment of mass = distance x mass, so it's the limit of ∑ (distance x ∆mass)