According to Newton’s second law, if a constant force operates on a particle for a particular time interval, the product of the force and the time interval (the impulse) equals the change in momentum.  Conservation of linear momentum is an essential principle in physics and other sciences. For example, when a ball is thrown horizontally into the air, the linear momentum gained by the ball must cancel out the linear momentum lost by the thrower.

Also massless particles cannot be destroyed but can only change forms. A famous example of this behaviour is a collision between two billiard balls on a pool table: The balls experience a change in their linear momentum resulting from their interaction with each other. Momentum is represented by →  p

Body : 

Linear Momentum of System of Particles

Listed below are some features of linear momentum and the process of calculating the linear momentum:

1. The formula of linear momentum is P = mv. 
2. Newton understood the importance of the component and highlighted the law of motion in terms of the same in his second law of motion. 
3. The second law of Newton describes the importance of momentum. It states that moment is applicable in any object considering the changing mass systems. However, the relationship between force and mass is more functional when the object’s mass is a constant factor. 
4. The second law of Newton considers various factors- the relationship of the change in mass and the force and the direction of the force. 
5. The formula of Newton’s second law for a single particle is F = dP/dt, where  F denotes the force of the concerned particle. If the number of particles in the momentum is n, the formula becomes 

P = P1 + P2 +….+Pn.

 The momentum is written as P = m1 v1 + m2v2 + ….+mnvn. 

P = ∑mnvn

P = MV

1. The centre of the object’s mass lies on the plane of symmetry.
2.  The centre of the object’s mass does not necessarily need to lie within the same thing. It may be located anywhere inside or outside the particle. 

Conservation of linear momentum

According to the conservation of momentum principle, if no net external force is acting on a body or a system of bodies then its net linear momentum remains constant. That is, two objects colliding have the same combined momentum before and after the collision. Momentum is always conserved in an isolated system collision. Your hand receives the ball’s kinetic energy when you catch it, just like when you throw a baseball.

Thus, during collision, momentum can only be transferred from one body but another such that the total momentum of the combined system remains the same.

Pi= Pf

The Linear Momentum formula can be expressed as-

P = mv

P is also known as the Linear Momentum.

v is also known as the Linear Velocity.

And m is the mass of the body.

Requirements for conservation of momentum

However, there is a complication. For a system’s momentum to be conserved, it must meet two conditions:

• During the interaction, the system’s mass must remain constant. As the objects interact, by applying forces on each other, they may transfer mass from one to the other; however, any mass gained by one object must be offset by the loss of mass from another. As a result, the overall mass of the object system remains constant over time:

[dmdt]system=0

• The system’s net external force must be zero. As a result, each internal force’s momentum change is cancelled by another momentum change of equal magnitude but opposite direction. As a result, internal forces cannot change a system’s total momentum because the changes sum to zero. 

It can be mathematically expressed by-

  dPdt  =  d(mv)dt

           = mdvdt

           =  ma

           =  Fnet

Applications of law of conservation of linear momentum

Conservation of momentum is a fundamental law of physics that deals with the relationship between an object’s mass and velocity. This principle can be derived from Newton’s laws of motion; in fact, conservation of momentum extends Newton’s second law of motion.

One of the most critical applications of conservation of momentum is the launching of rockets. The rocket fuel burns and pushes the exhaust gases downwards, and because of this, the missile also gets a push upwards. Motorboats also work on the same principle. It moves the water backwards and, as a result, gets pushed forwards in reaction to conserving momentum.

Traction applied to one side wheels or revolving axis causes a moving body like a bicycle to move forward. The same principle applies in a car where wheels push and pull the vehicle forward or backward under control by steering wheels.

Conservation of momentum states that if two bodies collide, their relative velocities before will be equal to their relative velocities after the collision. So, for example, it means that if two cars are moving towards each other at 20 mph, then after the collision, both will move away at 20 mph from each other.

Conclusion 

According to the law of conservation of linear momentum, if no net external force is acting on a body or a system of bodies then its net linear momentum remains constant. This concept is used to solve many problems, like that of rocket propulsion. The law of conservation of linear momentum can be easily related to Newton’s second law of motion.

dP/dt = Fnet  is the mathematical way to relate the two laws.