Finding Center of Mass - Plate with hole

In summary, a circular plate with a radius of 11 cm and a circular hole with a radius of 3 cm has its center of mass located at a distance of 4 cm from the origin along the x-axis. To find the center of mass, the mass of the plate and the hole can be treated as opposing forces acting on the plate, with the larger mass being located on the opposite side of the balance. This can then be translated into coordinates to determine the exact position of the center of mass.
  • #1
Bryon
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Homework Statement



https://wug-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?cc/DuPage/phys2111/fall/homework/Ch-09-Momentum/plate_with_hole/3.gif

A uniform circular plate of radius 11 cm has a circular hole of radius 3 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 mass = (m1x1 + m2x2)/ (m1 + m2)

Im really stumped with this one. I was thinking at first to find the total area of the plate and then subtract that from the area of the hole. I am at a loss with this one.
 
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  • #2
Almost right - imagine the hole as equivalent to a piece of metal that size/shape/position on the opposite side of the balnace.
 
  • #3
This one is really getting me. The center of mass will be away from the hole. Now to translate into coordinates.
 
  • #4
Imagine the force * distance downward for the mass of the entire plate, now imagine the hole is a mass * force upward
 
  • #5
So you essentially subract the larger mass from the other? I still don't see how to translate that into coordinates.
 

FAQ: Finding Center of Mass - Plate with hole

1. What is the center of mass of a plate with a hole in it?

The center of mass of a plate with a hole in it is the point at which the mass of the plate is evenly distributed. It is the point where the plate would balance if it were placed on a pivot.

2. How is the center of mass calculated for a plate with a hole?

The center of mass for a plate with a hole can be calculated by finding the individual centers of mass for each section of the plate (such as the solid portion and the hole), and then using the equation for weighted average to determine the overall center of mass.

3. Is the center of mass different for plates with different sized holes?

Yes, the center of mass will be different for plates with different sized holes. The size and location of the hole affect the distribution of mass and therefore, the location of the center of mass.

4. How does the shape of the plate affect the center of mass?

The shape of the plate can affect the location of the center of mass. For example, a plate with a square shape will have a different center of mass compared to a plate with a circular shape, even if they have the same dimensions and hole size.

5. Why is finding the center of mass important for a plate with a hole?

Finding the center of mass is important for a plate with a hole because it helps determine the stability and balance of the plate. Knowing the center of mass can also be useful in engineering and design applications, such as determining the best placement of a hole for optimal balance.

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