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

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To find the second moment of area for a rectangle with a circular cutout, the shape is defined as a rectangle measuring 8 units in horizontal length and 6 units in vertical height, with a circular cutout centered at (5,3). The discussion highlights the need for integration methods, specifically suggesting the use of integral y^2dxdy or integrating x^2dydx about the center of mass. Participants emphasize the importance of knowing the radius of the circle for accurate calculations. The focus remains on determining the second moment of area about the vertical axis, clarifying that the center of mass is not the primary concern. Understanding these calculations is essential for solving the problem effectively.
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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.
 
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Hello, does the photo look like the one I attached?
 

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mishek said:
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.
 
So, what is the question? What are you trying to find, the center of mass of the object?
 
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.
 
HallsofIvy said:
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
 
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