# Derivation of formula of centroid

1. Nov 23, 2015

### werson tan

1. The problem statement, all variables and given/known data
what is y ′and y bar ? why y ′ is changed to y bar ? why are they = 0 ?

2. Relevant equations

3. The attempt at a solution

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2. Nov 23, 2015

### J Hann

The middle integral is zero because y' is measured w.r.t. to the centroid so that
each value of y' dA is cancelled by -y' dA by definition of a centroid or in other
words y-bar = zero when measured from the centroid.
Also, since y' is measured from the centroid then the integral of y'^2 dA is just
the moment of inertia about the center of mass which is Ix.

3. Nov 23, 2015

### werson tan

in the first integral , the
in the first integral , the y prime is squared , so they dont cancel out each other?

4. Nov 23, 2015

### SteamKing

Staff Emeritus
When have you squared a real number and it came out negative?