Motion of the Center of Mass: Let us take the motion of a object of n particles of individual masses m1, m2, ......., mn and net mass M. It is assumed that no mass enters or leaves the object during its motion, so that M remains fixed. Then, as we have seen, we have the relation
![1095_motion of center of mass.png](https://www.expertsmind.com/../CMSImages/1095_motion of center of mass.png)
Or
![1109_motion of center of mass1.png](https://www.expertsmind.com/../CMSImages/1109_motion of center of mass1.png)
Differentiating this expression with related to time t, we have
![2208_motion of center of mass2.png](https://www.expertsmind.com/../CMSImages/2208_motion of center of mass2.png)
Since,
= velocity
Therefore,
... (i)
Or velocity of the Center of Mass is ![435_motion of center of mass5.png](https://www.expertsmind.com/../CMSImages/435_motion of center of mass5.png)
Or
Further,
= momentum of a particle
. Therefore, Eq. (i) can be written as
![96_motion of center of mass7.png](https://www.expertsmind.com/../CMSImages/96_motion of center of mass7.png)
Differentiating Eq. (i) with related to time t, we get
![132_motion of center of mass10.png](https://www.expertsmind.com/../CMSImages/132_motion of center of mass10.png)
Or
... (ii)
Or
Or
Further, in accordance with Newton's second law of motion
. Hence, Eq. (ii) can be written as
![1757_motion of center of mass14.png](https://www.expertsmind.com/../CMSImages/1757_motion of center of mass14.png)
Thus, as noticed out earlier also, the centre of mass of a object of particles moves as though it were a particle of mass same to that of the entire system with all the external forces operating directly on it.
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