Notes On Centre of Mass - CBSE Class 11 Physics
Let us consider a system of n particles, with masses m1, m2,… , mn and the  positions of these particles represented by (x1, y1, z1), (x2, y2, z2), …, (xn, yn, zn). If the centre of mass, C, is represented by the coordinates X, Y, and Z, then    The location of the centre of mass of a system of particles depends on the locations of constituent particles and their masses. The position of the centre of mass of a given system of particles is given by  where The centre of mass of a system of particles can be regarded as the mass weighted average location of the constituent particles. When we deal with rigid bodies of continuous distribution of matter we need to replace the summation symbol with an integral symbol. We can make use of symmetry considerations while finding the centre of mass of homogeneous and regular-shaped bodies. Based on symmetry considerations, we can prove that the centre of mass of a thin rod, uniform disc, uniform sphere and other such regular bodies lies at their geometric centre.

Summary

Let us consider a system of n particles, with masses m1, m2,… , mn and the  positions of these particles represented by (x1, y1, z1), (x2, y2, z2), …, (xn, yn, zn). If the centre of mass, C, is represented by the coordinates X, Y, and Z, then    The location of the centre of mass of a system of particles depends on the locations of constituent particles and their masses. The position of the centre of mass of a given system of particles is given by  where The centre of mass of a system of particles can be regarded as the mass weighted average location of the constituent particles. When we deal with rigid bodies of continuous distribution of matter we need to replace the summation symbol with an integral symbol. We can make use of symmetry considerations while finding the centre of mass of homogeneous and regular-shaped bodies. Based on symmetry considerations, we can prove that the centre of mass of a thin rod, uniform disc, uniform sphere and other such regular bodies lies at their geometric centre.

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