# Conservation of Momentum, Definition of Conservation of Momentum (For CBSE, ICSE, IAS, NET, NRA 2022)

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# Conservation of Momentum

## Definition of Conservation of Momentum

• It is a major law of physics which states that the momentum of a system is constant if no external forces are acting on the system.
• It is embodied in Newton՚s First Law or The Law of Inertia.
• This law of conservation of momentum is confirmed by an experiment and can even be mathematically deduced on the reasonable presumption that space is uniform.

## Conservation of Linear Momentum

Law of Conservation of Linear Momentum States That Total Momentum of the System is Always Conserved if No External Force Acts on an Object or System of Objects

### Conservation of Linear Momentum

Momentum of the Two Balls Before Collision,

Total Momentum of the System of Two Balls Before Collision,

• During the Collision Exerts an Action Force on .
• In Response, from Newton՚s Third Law, Exerts a Reaction on , That is, , Such That
• Negative Sign Implies That the Two Forces Are Directed in Opposite Directions.
• After the Collision They Undergo Change in Velocity and the Corresponding Change in Momentum.
• Momentum of the Two Balls After Collision

Total Momentum of the System of Two Balls After Collision,

Also, from Newton՚s Second Law

Force

Similarly,

From Newton՚s third law,

• Total Momentum Before Collision = Total Momentum After Collision Hence this Equation Implies That if No External Force Acts on the System of Two Colliding Balls, the Total Momentum is Conserved.
• Even though the Momentum of Each Particle Changes, Altogether the Momentum of the System Remains Constant as Long as There is No External Force Acting on It.
• In a Head-to-Head Car Accident, the Momentum is Transferred from One Car to the Other, though So Much Force is Applied That the Car Structure Cannot Handle It, therefore a Car Wrecks.
• If the Cars Were Able to Deal with the Amount of Force, and the Collision Was Elastic They Both Will Move in Opposite Directions, Considering Their Weights Are Same.
• So, Momentum is Always Conserved in Any Collision, Whether It Be Elastic or a Non-Elastic Collision, though Kinetic Energy is Not Conserved in a Non-Elastic Collision, the Kinetic Energy is Converted into Heat Energy or Potential Energy Etc.

## Example of Conservation of Momentum

• Let՚s take the example of a balloon, the particles of gas move rapidly colliding with each other and the walls of the balloon, even though the particles themselves move faster and slower when they lose or gain momentum when they collide, the total momentum of the system remains the same.
• So, the balloon doesn՚t change in size, if we add external energy by heating it, the balloon should expand because it increases the velocity of the particles and this increases their momentum, in turn, increasing the force exerted by them on the walls of the balloon.

## Application of Law of Conservation of Momentum

• The energy of a system is always conserved, one of the best applications of the law of conservation of momentum would be in space travel, there is no medium in space to exert a force on, then how do rockets travel
• They eject matter at very high speed so in an isolated system the momentum should remain constant therefore the rocket will move in the opposite direction with the same momentum as that of the exhaust.

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