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For a continuous system of matter Equation (1) becomes

In Cartesian components :

The computations for C.M. are usually tedious, but when the distribution of matter is symmetric about any axis, then the C.M. must lie on that axis; If more than one intersecting axes of symmetries exist than the point of intersection must be the centre of mass. This is obvious consequence of C.M. lying on the axis of symmetry.

Thus the C.M. of ring, disc, rod, cylinder, sphere etc. are their respective geometric centers.

Equivalence of system to C.M. in case of translational motion

For Kth particle in the system,



3.1 Dynamics of a particle
3.2 Dynamics of a system of particles
3.3 Law of Conservation of Momentum

Chapter 4

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