# Parallel axis theorem for area

1. Nov 5, 2015

### goldfish9776

1. The problem statement, all variables and given/known data
why the y bar is 0 ? according to the diagram , y ' has certain value , it's not 0 ! can someone help to explain ?

2. Relevant equations

3. The attempt at a solution

File size:
87.1 KB
Views:
53
2. Nov 5, 2015

### HallsofIvy

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

3. Nov 5, 2015

### goldfish9776

it pass thru centroid , why it is 0 ?

4. Nov 5, 2015

### haruspex

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.

5. Nov 5, 2015

### goldfish9776

why only the second integral = 0 , why not the first integral equal to 0 also ?

6. Nov 5, 2015

### SteamKing

Staff Emeritus
Because in the first integral, y' is squared.

When y' is by itself, you are adding products of y' dA on either side of the centroidal axis, so some products are negative and some are positive. When you calculate y'2 dA, all of the products are positive, so their sum adds up to a positive, non-zero result.