# Center of Mass

cmrgator

## Main Question or Discussion Point

Imagine a square with side length "a". Now, divide the square into 4 equal squares with side length "a/2". In the top righthand corner of the large square, a circle with radius "a/4" is cut out, which also removes the top corner piece. What is the new center of mass? (The origin is at the center of the large square). Thanks for your help!

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Here is an easy way to think about it.

Cut the circle out of the remaing 3 quarters of the large square, now you have a symmetrical shape about both x and y axis. The center of mass is the center, so we can now ignore this part.

Now what is the center of mass of the 3 circles?

Sorry, I don't see how that helps because of the cut out corner piece.
Anyway, even with the corner piece, I wouldn't know what to do.

Oops, I missed the part about the corner cut out...

I guess its back to x_bar y_bar in the first place then....

Well, it could still be done the way I was suggesting, don't know if its any easier though....but the point was to take out all area symmetrical about both axis, to simplify the problem.

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