Center of Mass: Plate with hole

AI Thread Summary
To find the center of mass of a uniform circular plate with a hole, it can be modeled as the difference between two disks: the larger disk representing the full plate and the smaller disk representing the hole. The formula for the center of mass is used, incorporating the masses and positions of both disks. The hole's position along the x-axis affects the overall center of mass, shifting it from the origin. Understanding this concept simplifies the calculation by treating the problem as a subtraction of mass. The final position of the center of mass can be determined using the provided equations and values.
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Homework Statement



A uniform circular plate of radius 14 cm has a circular hole of radius 2 cm cut out of it. The center of the plate is at the origin of the coordinate system and the center of the hole is located along the x-axis a distance 4 cm from the origin. What is the position of the center of mass of the plate with the hole in it?

Homework Equations



Center of Mass (x)= (m1x1+m2x2)/(m1+m2)

The Attempt at a Solution


This one has me confused. I know that the hole will move the center of mass, but I'm not sure how. Any help would be appreciated! Thanks!
 
Physics news on Phys.org
Finding the center of mass of two uniform disks would be easy (I hope you'll agree). How can you represent the plate with hole as two uniform disks? Hint: 1 - 1 = 0.
 

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