Derivation of the motion of center of mass - Physics - System Of Particles And Rotational Motion

Question

Derivation of the motion of center of mass

Sayantan · Accepted Answer

Dear Student, Let in a system of many particles the co-ordinates of centre of mass of the system be (Xcm,Ycm,Zcm) then position vector of centre of mass would be Rcm=Xcmi+Ycmj+Zcmk (1) and position vectors of various particles would be EQ

(2) Motion of centre of mass Differentiating equation 1 we get

p is the vector sum of linear momentum of various particles of the system or it is the total linear momentum of the system If no external force is acting on the system then its linear momentum remains constant Hence in absence of external force

In the absence of external force velocity of centre of mass of the system remains constant or we can say that centre of mass moves with the constant velocity in absence of external force.
Hence from equation 18 we came to know that the total linear momentum of the system is equal to the product of the total mass of the system and the velocity of the centre of mass of the system which remains constant.
Thus in the absence of the external force it is not necessary that momentum of individual particles of system like p₁ , p₂ , p₃ . . . . . . . . . . . p_n etc. remains constant but their vector sum always remains constant.

Regards.