Coordinates of Center of Mass Vector Form

Centre of mass is a point of a system and its coordinates can be expressed in the vector format. Center of mass is a point of system which can be used to represent the motion of the system.We have learned in the previous post that, we can derive mathematical derivation of centre of mass location and it is some where in between the system of two bodies. It can be understood that the center of mass point is towards the heavy mass location of the system.

For a one dimensional body mass is along only one dimension like length and the center of mass has only one coordinate, may be along X-axis or Y-axis.

If the body is in a plane, its mass is spread over two dimensions and hence its center of mass also has two coordinates.To express the center of mass, we need at least two coordinates. If the system is in the three dimensions, then the center of mass of this system also has three coordinates.

Center of mass of a system can be identified even for a system with large number of particles just by extending the mathematical format.

We can express coordinates of center of mass in the mathematical vector format also. By adding unit vectors along each direction of the coordinate system, we can assign a vector format as shown in the video below.

To measure the magnitude of center of mass, we can find the vector magnitude of center of mass system as shown.