Relation Between Position Vectors Of Particles and Centre Of Mass

 

We can also define centre of mass in terms of vector. let rᵢ be the position vector of the ith particle and R be the position vector of the centre of mass, then

Centre Of Mass Of Rigid Continuous Bodies

For a real body which is a continuous distribution of matter, point masses are then differential mass elements dm and centre of mass is defined as

If origin is the co-ordinate of centre of mass, then

∫x dm = ∫y dm =∫z dm = 0

Centre Of Mass Of A Uniform Thin Road

We consider a uniform thin rod AB of mass M and length L. The rod is held along x-axis with its end A at the origin whose co-ordinate is (0,0). Let the element is placed side by side of length dx at distance x from the origin, then

Thus, it means that the centre of mass of thin rod AB lies at point (L/2,0) i.e Centre between its end A and B.