How Do You Calculate the Center of Mass for a Composite Shape?

AI Thread Summary
To calculate the center of mass for a composite shape, the relevant equation is x = 1/M ∑ x dm, where mass is not needed as it cancels out. The discussion emphasizes the importance of treating the shape as a point mass at its center of mass after determining its coordinates. It suggests analyzing each axis separately and using convenient reference axes for calculations. Additionally, considering the composite shape as a square combined with another square of negative mass simplifies the process. Understanding these concepts will facilitate finding the center of mass effectively.
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Homework Statement



What is the x and y coordinates of the center of mass for the uniform steel plate shown in the figure ?

Homework Equations



x=1/M \sum x dm

The Attempt at a Solution



I am not really sure how to being this one. Mass isn't given so I am not sure where to start. I feel like this will be really easy to do but I am just not sure how to begin it. I appreciate any help. Thanks!
 

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You won't need the mass, it will cancel out.

You didn't attach a figure.

Please show an attempt at a solution using your knowledge of your relevant equation. Look at each axis separately, and choose convenient ones as reference axes.
 
Here are two helpful tips:

1. The center of mass equation is linear. This means that once you find the center of mass of an object, you can treat the object as a point mass located at its center of mass.

2. For this question, it's easier to consider the object as a square combined with another square of negative mass.
 

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