# Law of Conservation of Momentum

Let’s start the introduction of the law of Conservation of Momentum

Contents

## Law of Conservation of Momentum

Law of Conservation of Momentum- It states that for two objects colliding in an isolated system, the total momentum before and after the collision is equal. This is because the momentum lost by one body is equal to the momentum gained by the other.

• This law means that whenever one body gains momentum, then some other body must lose an equal amount of momentum.
• Momentum is never created or destroyed.
• The law of conservation of momentum is also called the principle of conservation of momentum.
•  It is an important consequence of Newton’s third law of motion.

### Examples of  conservation of momentum

• System of gun and bullet
• A rocket also works on the principle of conservation of momentum.
• A jet airplane also works on the principle of conservation of momentum.

### Derivation of conservation of momentum

Consider two colliding particles A and B whose masses m 1 and m 2 with initial and final velocities as u 1 and v 1 of A and u 2 and v 2 of B. The time of contact between two particles ‘t’. ### In the case of gun and bullet system

When a bullet has fired a gun, the gun exerts a force on the bullet in the forward direction. This is the action force. The bullet exerts an equal force on the gun but in the opposite direction.

This is the reaction force. Due to the large mass of the gun, it moves only a little distance backward by giving a jerk at the shoulder of the gunman or soldier. The backward movement of the gun is known as the recoil velocity of the gun.

According to the law of conservation of momentum:

The momentum of bullet = Momentum of gun

Mass of bullet x Velocity of bullet = Mass of gun x Recoil velocity of the gun

Recoil velocity of gun: The backward velocity of the gun is called recoil velocity.

## Momentum

The momentum of a particle represented by the letter ‘p’ is the product of two quantities: mass and velocity.

Momentum = mass x velocity

p = m x v

• The SI unit of momentum is kg.m/s
• Momentum is a vector quantity.
• Every moving body possesses momentum.
• If a body is at rest, hence its momentum is also zero.

### Example of Momentum

A karate player can break a pile of tiles or slab of ice with a single blow of his hand because a karate player strikes the piles of tiles with his hand very, very fast. In doing so, the large momentum of the fast-moving hand is reduced to zero in a very, very short time. This exerts a very large force on the pile of tiles or the slab which is sufficient to break them apart.

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