Derivation of formula of centroid

[werson tan]

Homework Statement

what is y ′and y bar ? why y ′ is changed to y bar ? why are they = 0 ?

Homework Equations

The Attempt at a Solution

 

[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 canceled 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.

 

[werson tan]

The middle integral is zero because y' is measured w.r.t. to the centroid so that
each value of y' dA is canceled 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 ^2 dA is just
the moment of inertia about the center of mass which is Ix.

in the first integral , the

The middle integral is zero because y' is measured w.r.t. to the centroid so that
each value of y' dA is canceled 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.

in the first integral , the y prime is squared , so they don't cancel out each other?

 

[SteamKing]

in the first integral , the

in the first integral , the y prime is squared , so they don't cancel out each other?

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