Why ain't momentum conserved when external force acts on the system?
Please explain with an example.
Momentum is the mass of the object times the velocity. Force is defined as the mass of an object times the change in velocity. If the system is exposed to an external force, the velocity of the system changes. Since the velocity of the system changes, so too does the momentum hence it is no longer conserved.
If your system is a single billiards table with one ball and no momentum, applying a force to the table will cause the ball to move.
Why do you think it should be conserved? Do you know how conservation of momentum is derived?
dP/dt = 0 = F (external). hence P is constant.
Only time this is true is the case Fexternal = 0, hence no external force.
Momentum is conserved in a system that includes all the sources of your 'external force'.
That is the basis of COM. There is no contradiction or exception.
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