Motion of Centre of Mass and linear momentum conservation of Centre of mass.

Motion of centre of Mass:
It is clear from above equation that C.M. of system of particles moves as a particle of mass equal to that of the whole system (M) with all the external forces acting directly on it.
Some Important Points related to motion of C.M.
a) If centre of mass of a system is at rest and net external force acting on the system is zero, then the C.M. will continue be in rest position even few particles may move in the direction of force acting on these individual particles.
b) Motion of C.M. of a system or object is not affected by any of internal forces as they always make action and reaction pairs, so their net contribution to system is zero.
c) If two particles placed on smooth surface separated by certain distance and they move towards each other due to mutual attractive force, then
d) In the absence of any external force, the acceleration of CM is zero, irrespective of individual acceleration of particles.
e) In the absence of external force, the velocity of CM is also constant.
f) Under the action of external force, the CM moves just as all the mass were concentrated at that point.

Linear Momentum of a system of particles:
Thus, the total linear momentum of a system of particles is equal to the product of the total mass of system and velocity of its centre of mass.
Conservation of Linear Momentum for system of particles:
According to law of conservation of linear momentum, total linear momentum of a system of particles remains constant or conserved in the absence of any external force.
Total linear momentum of a system of particles,
P ⃗ = MV ⃗_cm

If F ⃗_ext = 0 then (d P ⃗)/dt = 0  P ⃗ = constant
∴ MV ⃗_cm = constant  V ⃗_cm = constant.
So, we conclude that, if net external force on the system is zero, the linear momentum of system is constant, hence C.M. will move with constant velocity.
Q. Three bodies having masses 5kg, 4kg and 2kg are moving with speeds 5m/s, 4m/s and 2m/s, respectively along x-axis. What is magnitude of velocity of centre of mass of system?
Ans 45/11 m/s
Please see the complete video.



The videos will contain the content as per the CBSE board. The content will also help to those students who are going to appear in NEET or JEE Exams.