# Finding Mass Center of a Circular Disc with Hole & Weight

• Roadtrip
In summary, the conversation discusses the location of the center of mass on a uniform circular disk with a hole, after adding a weight at a specific point. The system is suspended and in equilibrium, with the center of mass located on a line going from the suspension point downwards. The value of K is to be determined.
Roadtrip
Why do we take the Center of mass to be on the right side rather than on the left?
A uniform circular disc of radius 4a with a circular hole of radius 2a made in the disc.
The mass of L is m and a particle of mass km is now fixed to L at the point P. The system is now suspended from the point S and hangs freely in equilibrium. The diameter ST makes an angle a with the downward vertical through S, where tana=5/6
Find the value of K

Disc before adding weight km at point P has a mass m of coordinates (10/3,0).
https://s26.postimg.org/qczk9oc3t/image.jpg[URL]https://s26.postimg.org/lsdduqseh/image.jpg

Last edited:
Roadtrip said:
I am having difficulty uploading a picture
You can use the "upload" button here, or upload it at some image hoster and add a link here.

I don't see images in the linked thread.

The center of mass is on a line that goes from S downwards. If P is lower than Q, then it is to the right of the geometric center of the large disk. It does not have to be - for small values of k the hole is more important and the center of mass would be to the left.

## 1. What is the purpose of finding the mass center of a circular disc with hole and weight?

The mass center, also known as the center of mass, is the point at which the mass of an object is evenly distributed in all directions. This is an important concept in physics and engineering, as it helps in understanding the stability and balance of an object.

## 2. How is the mass center of a circular disc with hole and weight calculated?

The mass center of a circular disc with hole and weight can be calculated using the formula: xcm = (A1x1 + A2x2 + ... + Anxn) / (A1 + A2 + ... + An) where xcm is the distance of the mass center from the reference point, A is the area of each component, and x is the distance of each component from the reference point.

## 3. What factors can affect the location of the mass center?

The location of the mass center can be affected by the distribution of weight or mass within the object, as well as any external forces acting on the object. Additionally, the shape and size of the object can also impact the location of the mass center.

## 4. Why is it important to accurately find the mass center of an object?

Knowing the exact location of the mass center is crucial in determining the stability and balance of an object. This information is used in various fields such as engineering, physics, and even sports, to ensure that structures, machines, and equipment are properly designed and functioning.

## 5. Can the mass center of an object change?

Yes, the mass center of an object can change if the distribution of weight or mass within the object is altered, or if external forces are applied to the object. For example, if additional weight is added to one side of an object, the mass center will shift towards that side.

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