How can I derive the equation X(cm) = int(X dm)/M?

[Dweirdo]

OMG second time I'm opening a thread in the wrong forum FFS!
Damn bookmarks! MODS move it please.

Homework Statement

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).

Homework Equations

X(cm)=sigma(Xi Dmi)/M

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 !

 

[tiny-tim]

Hi Dweirdo!

(have a sigma: ∑ and a delta: ∆ and an integral: ∫ and try using the X₂ tag just above the Reply box )

… 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?

How does ∑ X_i ∆m_i become ∫ X dm ?

Because that's what an ∫ is …

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

 

[Dweirdo]

Hi Dweirdo!

(have a sigma: ∑ and a delta: ∆ and an integral: ∫ and try using the X₂ tag just above the Reply box )


How does ∑ X_i ∆m_i become ∫ X dm ?

Because that's what an ∫ is …

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

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 :}

 

[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)