Find Center of Gravity Distances for Cut Discs

In summary, the conversation discusses the calculation of the distance between two centers of gravity before and after a disc is cut. The disc A has a radius of 2m and the cut out disc has a radius of 1m. The mass of the discs is proportional to their areas and the center of gravity is balanced at the center of disc A. The calculated distance between the two centers of gravity is approximately 0.333m and there is some uncertainty about the correctness of the answer. The method used could be checked by cutting out an identical hole in the left half and checking if the center of gravity remains in the middle.
  • #1
crossfacer
21
0

Homework Statement


A unifrom disc A of radius 2m is cut as shown in the image. The cut out is also a disc of radius 1m. Find the distance of the two center of gravity before and after the paper disc is cut.

http://crossfacer.com/circle.jpg

Homework Equations



x=m1x1/M+m2x2/M+...

The Attempt at a Solution



Mass of the disc is proportional to its area.
so mass of disc A=2^2pi=4pi units
mass of disc being cut out=1^2pi=pi units

Let x be the distance between the two centers of gravity.
(4pi-pi)(2-x)=(4pi)(2)-(2+1)(pi)
x=0.333m

This question is quite difficult for me. I don't have much confidence on my answer.:-p May anyone try it?:smile:
 
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  • #2
Your answer looks correct in my book.

You assume the homogeneity of the disc, and thus mass is proportional to the area. You know that together, they produce a center of gravity balanced at the center of disc A, and your equations reflect that.
 
  • #3
mezarashi said:
Your answer looks correct in my book.

You assume the homogeneity of the disc, and thus mass is proportional to the area. You know that together, they produce a center of gravity balanced at the center of disc A, and your equations reflect that.

I feel like my answer is not correct:frown:. I guess x should be about 0.5.
 
  • #4
well to check maybe you could use same methods with your new result and cut out identical hole in left half. I think it will end up in the middle again.
 

Related to Find Center of Gravity Distances for Cut Discs

1. What is the center of gravity of a cut disc?

The center of gravity of a cut disc is the point where the disc's weight is evenly distributed in all directions. This point is also known as the centroid of the disc.

2. How do you find the center of gravity of a cut disc?

To find the center of gravity of a cut disc, you need to determine the distance of the disc's center from its edges. This can be done by measuring the diameter of the disc and then dividing it by two. The resulting distance is the radius of the disc. Next, measure the distance from the center of the disc to its edge. This distance is known as the radius of the cut disc. The center of gravity can then be calculated using the formula: center of gravity = (radius of the disc - radius of the cut disc)/2.

3. Why is it important to find the center of gravity of a cut disc?

The center of gravity of a cut disc is important because it determines how the disc will balance and rotate. This information is crucial for engineers and designers to ensure the stability and performance of objects that use cut discs, such as wheels, gears, and propellers.

4. What factors can affect the center of gravity of a cut disc?

The center of gravity of a cut disc can be affected by several factors, including the shape and size of the disc, the material it is made of, and the location and size of the cut. Any changes to these factors can alter the disc's center of gravity, which can impact its balance and stability.

5. Are there any tools or techniques to help find the center of gravity of a cut disc?

Yes, there are various tools and techniques that can be used to find the center of gravity of a cut disc. These include mathematical calculations, physical balancing methods, and computer simulations. The most appropriate method to use will depend on the specific properties and requirements of the disc.

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