The law of conservation of momentum is the most useful law in all laws of physics. Let's learn more about quick save and its origin and solved problems.

Law of conservation of momentum

It states that

The total momentum of a system is always conserved for an isolated system

Now we will have to know that what isolated system is

Isolated system is the system whom does not interact with their surroundings and will remains constant

This law is directly related to the third law of motion

It states that

Every action has an equal but opposite reaction

The law of conservation of momentum has been fully confirmed by experiments and can even be deduced mathematically under the reasonable assumption of a uniform space. This law applies to all types of interactions between objects, including collisions between particles, interactions between electromagnetic fields and particles, and gravitational interactions between objects. The conservation of momentum is an essential principle in many areas of physics, including mechanics, electromagnetism, and quantum mechanics, and is widely used in the design and analysis of complex physical systems.

Example of the law of conservation of momentum

Here are examples of the law of conservation of momentum:

• Air-filled balloons
• System of gun and bullet
• Motion of rockets

Mathematically it can be described as

Newton's third law states that for the force exerted by object A on object B, object B exerts an equal and opposite force backwards.

Consider two colliding particles A and B of masses m₁ and m₂, with initial and final velocities u₁ and v₁ for A and u₂ and v₂ for B, respectively. The contact time between the two particles is t.

A = m₁ (v₁ - u₁)

B = m₂ (v₂ - u₂)

And also the according to newton’s third law of motion

F = -F

So the related term that we get from it is the

m₁ u₁ + m₂ u_{2 =} m₁ v₁ + m₂ v₂ 

Where

m₁ u₁ + m₂ u₂   = total momentum before collision of particles A and B

m₁ v₁ + m₂ v₂   = total momentum after collision of particles A and B

So from the above equation we can say that the law of conservation of momentum is conserved.

 

Conservation of Momentum Example

       Consider this balloon example, the gas particles are moving fast and collide with each other and the wall of the balloon, even though the particles themselves are moving faster or slower when they lose or gain momentum in collisions, the total momentum of the system remains the same.

So the size of the balloon does not change, if we increase the external energy by heating it, the balloon should expand, because it increases the speed of the particles, which at in turn increases their momentum, increasing the force they exert on the walls of the balloon.