Kinematics-Laws of Motion-Linear Momentum

Linear momentum in physics is the value obtained by the product of any system’s mass with its velocity. Thus, we can say that it is directly proportional to both mass and velocity. It is a vector quantity (a quantity that has both magnitude and direction). The symbol used for denoting ‘p’, and its unit is kilogram metre per second (kg. m/s). Newton’s second law of motion has a great relationship with momentum. The frame of reference has a diverse effect on momentum. However, in a closed system, i.e., a system in which there is no exchange or transfer of matter, there will be no momentum change too. Momentum has a great role in different physics branches, such as electrodynamics, quantum mechanics, quantum field theory, etc. 

The formula of linear momentum

As already discussed, momentum is the product of the mass and velocity of a given system.

Therefore, the linear momentum formula shall be as follows:

p=mv

where p= Linear momentum,

m= mass of the particle and

v= velocity of the particle.

From the linear momentum formula, it is clear that it is directly proportional to mass and velocity. Moreover, mass is scalar, whereas velocity and momentum both are vector quantities. Therefore, the momentum direction will be equal to the velocity direction as mass has no direction but only magnitude. So we can conclude that if velocity is negative, then the momentum will also be in a negative direction. Similarly, if the velocity is towards the motion, i.e., positive direction, then momentum will also be positive.

Impulse momentum theorem

According to the Impulse momentum theorem, the change of momentum is always equal to the impulse experienced by the given body.

F.Δt = m(vf) –m (vi)

m(vi)= initial momentum

m(vf)= final momentum

Say, the initial and final momentum remains unchanged, then the equation shall be as:

F.Δt = m (vf – vi)

The impulse-momentum theorem tells us that the force with a small velocity for a long time can produce the same velocity as the greater force for a short time.

Linear momentum and Newton’s Second Law of Motion

Newton’s second law of motion is in great reference with momentum. The second law is as Fnet= m. a. 

The change in external force is equal to the change of momentum concerning the net time of change. Thus, we can say that the net change in momentum will be equal to the difference between final and initial momentum. 

Fnet= Δp/Δt

Substitute the acceleration and momentum, we get:

Δp=Δ(mv)

If the system has constant mass, the equation shall be as:

Δ(mv)=mΔv.

Substituting, p=mv as Δp= Δ(mv), we get:

Fnet= mΔv/Δt

We know that a = Δv/Δt

Substituting it in the equation, we get:

 Fnet= m.a

Conservation of linear momentum

Conservation of linear momentum states that in an isolated system, the system’s total momentum remains unchanged. The total momentum of any system is the sum of the individual momenta of several objects. The conservation of linear momentum applies to different interactions such as collisions and separations due to explosive forces.

Application of Conservation of Linear Momentum

The conservation of linear momentum has several applications in our daily life. 

• For example, in the launching of rockets. When the rocket fuel burns, it pushes the in a downward direction. We can say that the downward momentum of the exhaust gases becomes equal to the magnitude of upward momentum (of the rising rocket). Therefore, the net momentum remains constant. 
• In a collision and coalesce of two particles with known momentum, this law can help determine the momentum of the coalesced body. This law is also helpful in determining the momentum of another particle if the momentum of one particle after the collision is known. Similarly, if we know the total kinetic energy after the collision, we may determine the momentum of particles separately.

Conclusion 

Linear momentum in physics is the value obtained by the product of any system’s mass with its velocity. Thus, we can say that it is directly proportional to both mass and velocity. It is a vector quantity (a quantity that has both magnitude and direction). Moreover, mass is scalar, whereas velocity and momentum both are vector quantities. Therefore, the direction of momentum will be equal to the direction of velocity. So we can conclude that if velocity is negative, then the momentum will also be in a negative direction and vice-versa. The symbol used for denoting ‘p’, and its unit is kilogram metre per second (kg. m/s). The linear momentum formula shall be as follows: p=mv. Conservation of linear momentum states that in an isolated system, the total momentum of the system remains unchanged.