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Centre of Mass of a Rigid Body : Centre of Mass of a Circular Ring, Disc, Rod and Sphere

The centre of mass of a rigid body is a point at a fixed position with respect to the body as a whole. The position of the centre of mass of a body depends on its shape and the way and mass is distributed in the body.

Depending upon these two factors, the centre of mass may lie within the body or even outside it. If the body has a regular geometrical shape and if its mass distribution (i. e. density) is uniform, it is easy to locate the position of its centre of mass.

For example,
  • The centre of mass of a uniform sphere is at its geometrical centre. 
  • For a thin rod of a uniform cross-section and density, the centre of mass is at its geometrical centre. 
  • For a thin circular plane ring, the centre of mass is again at its geometrical centre where there is actually no matter. This is an example of a body whose centre of mass lies outside the body. 
Thus, it is easy to locate the centre of mass of symmetrical bodies with uniform mass density. If we have a body which has an irregular shape or a non-uniform mass distribution, it is not easy to locate its centre of mass. The given figure shows the position of the centre of mass of some regular bodies.
The centre of mass of a thin triangular plate is at the point of intersection of the three medians (fig.a). 

For a right circular solid cone, the centre of mass is a point on its axis at a distance h/4 from its base, where h is the height of the cone (fig.b).

For every rigid body, the motion of its centre of mass can be determined in which the internal forces do not play any role. 
These internal inter-particle forces are always present, for otherwise the body would fall apart. But we need not consider these internal forces while analyzing the gross motion of the body, e. g. rotation and translation.





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