Law of Conservation of Linear Momentum

The linear momentum of a particle is defined as the product of the mass of the particle times the velocity of that particle. Conservation of momentum of a particle is a property exhibited by any particle where the total amount of momentum never changes. Linear momentum of a particle is a vector quantity and is denoted by

According to the conservation of linear momentum,

If the net external force acting on a system of bodies is zero, then the momentum of the system remains constant.

We have to remember that the momentum of the system is conserved and not that of the individual particles. The momentum of the individual bodies in the system might increase or decrease according to the situation, but the momentum of the system will always be conserved, as long as there is no external net force acting on it.

The principle of conservation of momentum states that if two objects collide, then the total momentum before and after the collision will be the same if there is no external force acting on the colliding objects.

The conservation of linear momentum formula mathematically expresses that the momentum of the system remains constant when the net external force is zero.
Initial momentum = Final momentum

Linear Momentum Formula

Linear momentum is mathematically expressed as:

You may also like to learn more about other related concepts as given below:

The law of conservation of momentum can be explained from the second law of motion. Newton’s second law of motion says that the rate of change of linear momentum of a body is equal to the net external force applied to it.

Mathematically it is expressed as:

If the net external force acting on a body is zero, then the rate of change of momentum is also zero, which means that there is no change in momentum.

Read More: Newton’s Second Law of Motion

Two bodies of mass M and m are moving in opposite directions with the velocities v. If they collide and move together after the collision, we have to find the velocity of the system.

Since there is no external force acting on the system of two bodies, momentum will be conserved.

Initial momentum = Final momentum

(Mv – mv) = (M+m)V_Final

From this equation, we can easily find the final velocity of the system.

One of the applications of conservation of momentum is the launching of rockets. The rocket fuel burns are pushes the exhaust gases downwards, and due to this, the rocket gets pushed upwards. Motorboats also work on the same principle, it pushes the water backward and gets pushed forward in reaction to conserve momentum.

Here is a video that explains the application of PCLM using an example of a bomb explosion

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