Application of Linear Momentum

In General the Linear momentum is the product of mass and velocity of a system. In equation form it is represented as:

p = mv.

We can see from the calculation that the force is directly proportional to the mass of the object (m) and the velocity (v). Therefore, the larger the object mass, the greater its velocity, and the greater its momentum. 

As we know that mass is a scalar Quantity. Since the momentum may be in negative direction, and if velocity is in positive direction then momentum will also be in positive direction. A large, fast-moving object has greater force than a small, slow object.

Momentum is a vector quantity and has the same direction as the velocity. The SI unit of force is kg m / s.

Newton’s second law of motion states that the rate of change in body momentum is equal to the total force acting on it. In General the momentum depends on the reference frame, but in any inertial frame it is a conserved value, which means that if an isolated system is not affected by external force, its total linear momentum is also not changed.

Momentum is also stored in a special relativity (in a modified formula) and, in a modified form, in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of the fundamental symmetries of space and time.

Conservation of Linear Momentum

In General the Linear Momentum of a Particle is the product of that particle’s Mass and Velocity. As energy is conserved linear momentum is also conserved under certain conditions. In order to provide the basis for the law of conservation of linear momentum, we will introduce the concept of linear impulse and use it to reformulate Newton’s second law.

In this new structure the net linear impulse represents the influence of the environment of the particle. Initially, we look at how the linear momentum of the particles changes in response to the external linear impulse. In order to conserve the linear momentum, the net external linear impulse must disappear.

Examples

Let us consider there are two bodies of weight M and m which are moving in opposite directions with velocity v. If they collide and move together after a collision, we have to find the velocity of the system.

Since there is no external force working on the two bodies, the momentum will be maintained or conserved.

That is:

Initial Momentum = Final Momentum.

Gun’s Recoil: When a bullet is fired from a gun, both bullets and gun are at rest, with zero Total momentum. When the bullet is fired, it rushes forward. As a result of conservation momentum, the cannon acquires a backward momentum. A bullet with a mass m is released at a moving speed of v. The mass M-shotgun achieves a velocity u. Hence the total momentum before firing a bullet from the gun is zero and after firing the momentum is again Zero.

Application of Conservation of Linear Momentum

One of the major applications of Conservation of Momentum is the launching of rockets. In General the rocket fuel is pushed out the exhaust gasses downwards, and as a result, the rocket is pushed upwards. 

One More thing is that the Motor boards also work with the same Principle, it pushes the water backward and gets pushed in reaction to conserve momentum. Hence this is some of the examples of Application of Linear momentum.

Conclusion

This topic basically focuses on Newtonian dynamics. Here the main concept that is defined is mass and velocity. The topic describes the law of linear momentum conservation. The total linear Momentum before an interaction is equal to the sum of the total linear Momentum after the interaction. 

In any system of objects which have less than zero external forces, the total linear momentum of the system remains constant. This topic relates that linear momentum is a vector Quantity. The force applied to an object changes only the momentum along the direction of force, the momentum component perpendicular to the direction of force is not affected.