How to Find the Second Moment of Area for a Rectangle with a Circular Cutout?

[jiboom]

Find the second moment of area about the vertical axis for the cross-section of the follwing shape.

i can't get the pic to paste so will describe it:

it is a rectangle of horizontal length 8 and vertical height 6.

if we let (0,0) be at the lhs bottom corner, then a circle has been cut out with
centre at (5,3)

i have no idea how to go about this. one web page says i need integral y^2dxdy another just used the c of mass of one shape and the other shape (was L shape). (so here i would need com of rectangle- com circle)

any help would be much appreciated.

 

[mishek]

Hello, does the photo look like the one I attached?

 

[jiboom]

Hello, does the photo look like the one I attached?

almost, the picture i have has the circle more towards the rhs of the rectangle.

 

[HallsofIvy]

So, what is the question? What are you trying to find, the center of mass of the object?

 

[haruspex]

You don't give the radius for the circle.
For the second moment about a vertical axis, don't you need to integrate x²dydx? And you might want that taken about the x coordinate of the mass centre.

 

[jiboom]

So, what is the question? What are you trying to find, the center of mass of the object?

as in my first post, i am trying to find the second moment of area about the vertical axis