# Newton's law and conservation of linear momentum

• savi
In summary, conservation of linear momentum is a consequence of both Newton's first and third laws. While the first law states that an object will continue in its original state of rest or uniform motion unless acted upon by an external force, the third law explains how the forces between two objects contribute to the conservation of momentum. Additionally, the second law provides a way to measure the change in motion caused by an external force. However, conservation of momentum is a fundamental principle that goes beyond just Newton's laws and is an important concept in understanding motion and interactions between objects.
savi
Conservation of linear momentum is consequence of which one of Newton's three laws?

What do you think?

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.

savi said:
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.

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

xboy said:
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

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

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..

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).

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?

## 1. What is Newton's Law of Conservation of Linear Momentum?

Newton's Law of Conservation of Linear Momentum states that the total momentum of a closed system remains constant over time, unless acted upon by an external force. In simpler terms, this means that in a system where there is no external force acting on it, the total amount of movement (momentum) will remain the same.

## 2. How does the law of conservation of linear momentum apply to everyday situations?

This law can be seen in everyday situations, such as when a car crashes into a stationary object. The car and the object will experience an equal and opposite force, resulting in a transfer of momentum. The total momentum of the system before and after the collision will remain the same, although it may be distributed differently between the car and the object.

## 3. Can the law of conservation of linear momentum be violated?

No, the law of conservation of linear momentum is a fundamental law of physics and has been proven to hold true in all observed situations. It is a law that applies to all systems, from the microscopic to the macroscopic level.

## 4. How is Newton's law of conservation of linear momentum related to Newton's second law of motion?

Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration, can be derived from the law of conservation of linear momentum. This is because, in a closed system, the change in momentum is equal to the net force acting on the system, divided by the time it takes for the force to act.

## 5. Are there any real-life applications of the law of conservation of linear momentum?

Yes, the law of conservation of linear momentum has many practical applications. For example, it is used in rocket propulsion systems, where the rocket's momentum is increased by expelling a high-speed exhaust in the opposite direction. It is also used in sports, such as in billiards or bowling, where the momentum of the ball is transferred to other objects in the system.

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