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I am studying momentum and I just want to check that I understand the idea correctly.

Think there's a system.In this system there's two masses ##m_1## and ##m_2## moving with some velocity ##\vec v_1## and ##\vec v_2## and they exert a forces each other.Lets call the total force acting on ##m_1## is ##\vec F_1## and for ##m_2## is ##\vec F_2##.

So If ##\vec F_1=\vec F^{ext}+\vec F_{21}##

##\vec F_2=\vec F^{ext}+\vec F_{12} ##

Then the change in the total momentum;

##Δ\vec P=\vec {(F_{tot})^{ext}} Δt##

If there's no exteral force then, ##Δ\vec P=0## .So If there's no external force then the change in momentum should be zero .If there's external force and its constant then the change in momentum will be constant but non-zero.##Δ\vec P≠0##

If the change in momentum is zero(No external force) the center of mass of the system will be not moving.If there's external force it will accelerate by ##\frac {\vec {(F_{tot})^{ext}} } {M}=a_{com}## (##M## here total mass of the system)

Just I am confused with the idea of external force...Think there's two object making projectile motion.and colliding in the air.Is the external force in here is gravity ? (No air drag)

How can we determine the external forces in a given system ?

Most collions happens in a small amount of time (##Δt## nearly ##0##), in this case can we say ##Δ\vec P=0## ? and If we can why ? (There will be external force)

Think there's a system.In this system there's two masses ##m_1## and ##m_2## moving with some velocity ##\vec v_1## and ##\vec v_2## and they exert a forces each other.Lets call the total force acting on ##m_1## is ##\vec F_1## and for ##m_2## is ##\vec F_2##.

So If ##\vec F_1=\vec F^{ext}+\vec F_{21}##

##\vec F_2=\vec F^{ext}+\vec F_{12} ##

Then the change in the total momentum;

##Δ\vec P=\vec {(F_{tot})^{ext}} Δt##

If there's no exteral force then, ##Δ\vec P=0## .So If there's no external force then the change in momentum should be zero .If there's external force and its constant then the change in momentum will be constant but non-zero.##Δ\vec P≠0##

If the change in momentum is zero(No external force) the center of mass of the system will be not moving.If there's external force it will accelerate by ##\frac {\vec {(F_{tot})^{ext}} } {M}=a_{com}## (##M## here total mass of the system)

Just I am confused with the idea of external force...Think there's two object making projectile motion.and colliding in the air.Is the external force in here is gravity ? (No air drag)

How can we determine the external forces in a given system ?

Most collions happens in a small amount of time (##Δt## nearly ##0##), in this case can we say ##Δ\vec P=0## ? and If we can why ? (There will be external force)

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