# Parallel axis theorem for area

## Homework Statement

why the y bar is 0 ? according to the diagram , y ' has certain value , it's not 0 ! can someone help to explain ?

## The Attempt at a Solution

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HallsofIvy
Homework Helper
$\overline{y}= 0$ because the y' axis, not the y axis, is defined as the vertical line passing through the center of mass.

haruspex
$\overline{y}= 0$ because the y' axis, not the y axis, is defined as the vertical line passing through the center of mass.
it pass thru centroid , why it is 0 ?

haruspex
Homework Helper
Gold Member
2020 Award
it pass thru centroid , why it is 0 ?
The shape can be thought of as made up of many little areas like A. Each little area has its own (x', y') coordinates relative to the centroid. y-bar is here defined as the average value of y' across all these little areas. By definition of centroid, that average is zero.

The shape can be thought of as made up of many little areas like A. Each little area has its own (x', y') coordinates relative to the centroid. y-bar is here defined as the average value of y' across all these little areas. By definition of centroid, that average is zero.
why only the second integral = 0 , why not the first integral equal to 0 also ?

SteamKing
Staff Emeritus