Finding the Center of Mass in a Divided Square

In summary, the conversation discusses finding the new center of mass after cutting out a circle from a square. It is suggested to cut the circle out of the remaining 3 quarters of the square to create a symmetrical shape, but this does not take into account the cut out corner piece. The conversation ends with a suggestion to simplify the problem by removing all areas symmetrical about both axes.
  • #1
cmrgator
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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  • #2
Here is an easy way to think about it.

Cut the circle out of the remaining 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?
 
  • #3
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.
 
  • #4
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.
 
Last edited:

1. What is the center of mass in a divided square?

The center of mass in a divided square is the point where the mass of the square is evenly distributed, meaning the square would balance perfectly if placed on that point.

2. How is the center of mass calculated in a divided square?

The center of mass in a divided square can be calculated by finding the average of the x-coordinates and the average of the y-coordinates of the individual parts of the square. These averages represent the coordinates of the center of mass.

3. Why is finding the center of mass important in physics?

Finding the center of mass is important in physics because it helps determine the overall behavior and stability of an object. It is also used in various calculations, such as calculating the torque and momentum of an object.

4. Can the center of mass be outside of the square?

No, the center of mass in a divided square will always be located within the boundaries of the square. This is because the individual parts of the square are symmetrically arranged around the center, making it impossible for the center of mass to be outside of the square.

5. How does the shape of the divided square affect the location of the center of mass?

The shape of the divided square does not affect the location of the center of mass. As long as the individual parts of the square are evenly distributed, the center of mass will always be located at the same point regardless of the shape of the square.

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