Why is the center of mass assumed to be on the vertical in an arc?

In summary, the center of mass in an arc is the point at which the entire mass of an object or system is concentrated. It is important in determining stability and analyzing motion and rotation. It can be calculated by finding the weighted average of all individual masses in the system. The center of mass may not always lie within the object or system and can change with changes in mass or distribution of mass.
  • #1
abdo799
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Homework Statement



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Homework Equations





The Attempt at a Solution


i have the solution , but in it , he assumes the center of mass is on the vertical and thus the distance of the vertical from the center is rsin(1/4∏)/(1/4∏) where r is the radius , so why did he take this assumption?
 

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  • #2
he assumes the center of mass is on the vertical ... so why did he take this assumption?
The wire is freely suspended from point A.
If the com was not vertically below point A, then what would happen?
 
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  • #3
Thanks, i got it
 
  • #4
Well done :)
 

What is the center of mass in an arc?

The center of mass in an arc is the point at which the entire mass of an object or system is considered to be concentrated. It is the point where the object or system would balance if it were subjected to a uniform gravitational field.

Why is the center of mass important in arcs?

The center of mass is important in arcs because it helps determine the stability and balance of the object or system. It also plays a crucial role in analyzing the motion and rotation of objects in an arc.

How is the center of mass calculated in an arc?

The center of mass in an arc can be calculated by finding the weighted average of all the individual masses in the system. This can be done using the formula: xcm = (m1x1 + m2x2 + ... + mnxn) / (m1 + m2 + ... + mn), where x is the position of each mass and m is the mass of each object.

Does the center of mass always lie within the object or system?

No, the center of mass may not always lie within the object or system. In some cases, the center of mass may be outside the object or system, especially if the distribution of mass is not uniform.

How does the center of mass change in an arc with changing mass or distribution of mass?

The center of mass in an arc will move if the mass or distribution of mass changes. This is because the center of mass is determined by the weighted average of all the individual masses, so any changes in mass or distribution will affect its position.

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