# What is the Law Of Conservation Of Momentum? | derivation

Last updated on November 18th, 2021 at 02:48 pm

If there is no net external force on a system, the total momentum of the system remains constant. This is the law of conservation of momentum. (also known as the principle of conservation of momentum). Here, by the term momentum, we mean Linear Momentum.

When the net external force acting on a system is zero then we call that system an isolated system.

## State the Law of Conservation of Momentum | Linear momentum conservation law

The Law of conservation of momentum states that the total momentum of an isolated system is constant. Interactions within the system do not change the system’s total momentum. In other words, the total momentum of a system is conserved, if that system is subject to only internal forces.

## Derivation of the Law of Conservation of Momentum | Derive the principle of conservation of Linear Momentum

As per Newton’s 2nd Law of motion, force F = ∆p/∆t … (1)

[here, ∆p/∆t = (change in momentum)/(elapsed time) = rate of change of momentum]

In an isolated system, the **net external force** is zero, F = 0

Hence from equation (1) for that isolated system we get, ∆p/∆t = 0

this implies, ∆p = 0

or, change in momentum is zero

This means Momentum remains constant when the external force is zero or Momentum remains constant in an isolated system.

Thus we can mathematically derive *the law or principle of conservation of linear momentum*.

In a system of particles, in which each may have different amounts of momentum, the total momentum of the system is the (vector) sum of all the individual momenta.

### What is the equation for the law of conservation of linear momentum

**∆p = 0** or, change in momentum is zero in an isolated system.

### What is the condition for the law of conservation of linear momentum

The external force is to be zero or the system needs to be an isolated system if we have to apply this conservation law for linear momentum.

### What is an isolated system?

When the net external force acting on a system is zero then we call that system an *isolated system*.

## Principle of conservation of momentum from Newton’s second and third laws

The principle follows Newton’s second and third laws.

A version of Newton’s second law [ F = (mv-mu)/t ] says that the net force on an object equals its rate of change of momentum.

By Newton’s third law, forces always come in pairs, with forces of equal strength directed oppositely.

Now, let’s take one such force pair as an isolated system. Thus, this isolated system will have 2 internal forces of equal strength directed oppositely.

As a result, the net force in any isolated system consisting of a force pair is zero.

Hence, there will be no change in momentum for the system.

Thus the Principle of conservation of momentum can be proven from Newton’s second and third laws.

Now, **Read about** one application of the law conservation of momentum here: Newton’s Cradle

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