Newton's law and conservation of linear momentum

savi
Conservation of linear momentum is consequence of which one of Newton's three laws?

Mentor
What do you think?

savi
I think it is Newton's first law , because its statement itself says that until we apply an external force, a body continues to be in its original state of rest or of unifrm motion in straight line.
But one of my colleagues thinks that it is the third law, because action reaction forces are equal and the total external force on the system being zero , momentum is conserved.

Mentor
I think it is Newton's first law , because its statement itself says that until we apply an external force, a body continues to be in its original state of rest or of unifrm motion in straight line.
But it's not very interesting if a single body continues with uniform velocity, at least as far as conservation of momentum goes.
But one of my colleagues thinks that it is the third law, because action reaction forces are equal and the total external force on the system being zero , momentum is conserved.
Yes, it's the third law that leads to conservation of momentum. Consider a collision between two bodies. Since they exert equal and opposite forces on each other for the same time, they produce equal and opposite changes in momentum in each other--thus the total momentum of the system remains unchanged.

xboy
I think it would be fair to say that it's a consequence of both first and third laws.

spidey
I think it would be fair to say that it's a consequence of both first and third laws.

only third law is enough..

F1 = F2
ma1 = ma2
mdv1/dt = mdv2/dt
dmv1/dt = dmv2/dt
dp1/dt = dp2/dt
integrating with time dt gives,
p1 = p2

xboy
When you use F = ma, N1L is automatically implied, is it not.

spidey
obviously..but the question is "Conservation of linear momentum is consequence of which one of Newton's three laws?" .. so momentum conservation can be derived starting with N3L and using N2L...but N1L is a special case..

xboy
So you agree that you need to use another law.

The argument can be stated this way: Let us consider a system of particles. According to N1L none of the momentums of each particle remains constant unless forces act on it. Here the forces are all forces of interaction. So the total rate of change of momentum of the system is due to forces : f1 + f2 +f3+... which add up to zero (N3L). Because no net force is acting on the system , it's momentum is conserved (N1L).

vjraghavan
As far as I understand law of conservation of momentum is because of Newton's Laws of motion. It is difficult to say whether it is because of first, second or third alone. The three laws are not independent laws. They come as a whole and not individually, or one by one.

First law says that without external interference a particle continues to be in uniform motion or at rest in an inertial frame. The first law only mentions a property of matter, called inertia. It makes no explicit mention of momentum= mv. This is because it does not say anything about the mass= m. So I don't think that you can say Conservation of Linear Momentum is because of the first law alone.

Second law gives a measurement of such rate of change in motion and the resistance offered by the particle for such a change, namely the mass. This law gives a formula to calculate how the motion varies upon the action of an external agency. It also enables us to measure the property it defined in the first law, mass.

Third law explicitly mentions that any such external agency is necessarily an interaction between two particles (or systems). The third law is not just another law dealing with some other aspect of motion. But is a logical necessity which gives meaning to the first two laws.

Further still, conservation of momentum is more fundamental and wider than Newtons Laws. So are Newtons Laws a consequence of Conservation of Momentum or vice versa?