physical significance of the centre of mass of the system
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The center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses. For simple rigid objects with uniform density, the center of mass is located at the centroid.
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- Centre of mass is the unique point about which the moment of mass of a body or a system of particles is zero.
- The distribution of matter in the body or system of particles is symmetric about this point.
- It’s value depends upon the masses of the particles and the position of the particles relative to one another.
- A body is perfectly balanced at its center of mass.
- If a solid is made of homogenous material, that is the density is same everywhere, and has a regular shape, it’s center of mass is the point of symmetry or the geometrical center.
- Example: For a uniform rod, the center of mass is at its midpoint, for a ring, disc or sphere, it is at its Centre, for a rectangular lamina or thin plate, it is at the point of intersection of the diagonals, for rectangular parallelepiped, it is at the center or point of intersection of the four diagonals.
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