Newton’s third law of motion explains that when two objects in a closed system collide, their magnitude is always equal and the direction of the force applied is in the opposite direction of each other. The law of conservation of momentum means that the momentum at the beginning and at the end of a motion remains constant if the motion takes place in a closed system.

Difference between conservation of linear momentum and conservation of momentum

The momentum conservation law applies to all types of motions. Momentum is of two main types: angular and linear. While angular momentum describes the spinning momentum of the objects in motion, linear momentum is simply the product of an object’s mass and its speed. It possesses magnitude as well as direction and hence it is a vector quantity.  

Formula for linear momentum:  p = mv         

It is measured in units of kg m² s-¹.

Linear momentum describes the changes in the motion of a body relative to a reference point. Objects undergoing linear momentum move in a straight line unlike objects under angular momentum. In angular momentum, the objects do not travel in a straight line but they perform circular motions relative to a central point. For instance, take the revolution of earth around the sun. The earth is under angular momentum. 

Objects in linear momentum that have greater mass will require more force to change the momentum of the object in the system. While linear momentum can be changed by applying force, the angular momentum only changes when we apply torque to an object.

Examples of conservation of linear momentum

1. Pinballs: Before we release the ball from our hands, the pins are at rest. But when the ball hits the pins, all the pins fall due to the transfer of momentum from the balls to the pins. Hence, momentum is conserved.
2. Rocket propulsion: Before we launch a rocket, the momentum in it is zero as the rocket is at rest. At rest, the rocket has zero speed and hence the mass of the rocket multiplied by zero speed or velocity gives us a zero value. After we launch the rocket, the chemical energy that is stored as fuel in the rocket is burnt to transform into mechanical energy. This mechanical energy makes the rocket fly high against the earth’s surface. The fuel keeps burning, which results in the reduction of the mass of the rocket while the speed is increasing. Hence, the momentum in the rocket remains constant.
3. Gun and bullet system: A bullet at rest in the gun has zero momentum. After the bullet is fired, it gains momentum in the forward direction. The gun pushes backwards due to the momentum.
4. A cart and a person: A person sitting on a cart has zero momentum. When the person moves in front, the cart moves in the opposite direction to balance. To bring the momentum back to zero, the person must move back to the initial position at rest.
5. Billiard balls: When you hit the billiard ball with the cue stick, the momentum from the stick moves the ball forward and the ball, in turn, hits other balls in its way, which results in the transfer of momentum to the other balls. The momentum always remains conserved in the entire system.

Conclusion

It is a law of physics that every object that collides obeys the momentum conservation law. When we consider a closed system, momentum is conserved. This article describes the linear momentum conservation law and its relation to momentum conservation. We use equations of conservation of momentum to determine the velocity of an object or its mass. The constant nature of momentum in a motion helps us find the velocity of an object under motion and also gives us the initial momentum or the final momentum of the two objects.