# Parallel Axis Theorem problem help

1. Dec 7, 2013

### LeFerret

1. The problem statement, all variables and given/known data
This is moreof a conceptual question regarding the parallel axis theorem and area.
Lets say I have a solid rectangle with length L, and Width W.
I cut out a circle of radius R at the center.
When calculating the Total Area moment of inertia of the hollow region where the circle was cut out
because I know the region cut out has a negative area, so I subtract that moment of inertia from the rectangle's moment of inertia, but I'm not sure if that negative carries over inside the parenthesis as well

2. Relevant equations

3. The attempt at a solution

2. Dec 7, 2013

### SteamKing

Staff Emeritus
If you have a rectangle and then you remove a circular area from the center, the parallel axis theorem really doesn't come into play, because the centroid of the resulting figure hasn't changed from before the circular area was removed; i.e. I(net) = I(rectangle) - I(circle)

3. Dec 7, 2013

### LeFerret

I agree, but I wanted to explain what I was asking as simply as possible, the circle could be removed anywhere and it could be any series of shapes attached together. What I am confused on is if that negative area comes to play inside of the parenthesis or if it's |Ad^2|

4. Dec 8, 2013

### ehild

You cut out a positive area, that makes a negative contribution to the total moment of inertia.

The second equation is correct.

ehild

5. Dec 8, 2013

thank you!!

6. Dec 8, 2013

### ehild

You are welcome

ehild