o
If we increase the number of elements n , the element size Dmi decreases , and coordinates of COM is given by :
Where x , y , z = coordinates of COM of small element dm
o
The vector expression equivalent to these three scalar expressions is Where o o
R = position of COM of body r = position of COM of small element of mass dm
Consider a thin rod of length l , taking the origin to be at the geometric centre of the rod and x-axis to be along the length of the rod , we can say that on account of reflection symmetry , for every element dm of the rod at x , there is an element of the same mass dm located at – x .
The net contribution of every such pair to the integral and hence the integral x dm itself is zero . Thus the COM coincides with the geometric centre .