Concept of Center of Mass : Discrete Distribution of Mass
Let us consider a rigid body in motion. By definition, a rigid body consists of a number of particles separated by constant distances and cannot be distorted by application of any amount of force. In order to completely determine the state of motion of such a system (object), we need first to specify the motion of all the constituting particles of the system. Let this rigid body be composed of N number of particles of masses m 1 ,m 2 , .....,m N with position vectors r 1 , r 2 , ....., r N , respectively with respect to the origin O of an arbitrary co-ordinate system. If we want to find out the total momentum of this object, we will have to add the momenta of all its constituent particles. Mathematically this can be done in the following way : Similarly if we want to find out the total kinetic energy of the object, we will have to add the individual kinetic energies of all the constituent particles :