Momentum Vector

Introduction:

Measurement of motion of a body can be explained by momentum vector.

Definition of momentum vector:

Momentum vector is defined as the total motion contained in the body. Mathematically, momentum vector is equal to the product of mass of the body and its velocity.
P = m × v
Where m is the mass of the body and v be the velocity of the body.
Momentum vector is a vector quantity. The unit of momentum vector is kg m /s in MKS and g cm /s in CGS.

Principle of Conservation of Momentum Vector:

It states that if no external force is applied on a system, then the momentum of the system remains constant. In other words, if there is no external force applied on the system,
the initial momentum of the system will be equal to the final momentum of the system Consider a system of two bodies on which there is no external force acting on it. Because the system is isolated from the surroundings, so it interacts only due to their mutual interactions. Due to the mutual interaction, the momentum of the individual bodies may change but the total momentum of the system remains constant. If q₁ and q₂ be their individual momentum's, then
q₁ + q₂ = constant
For a system of n bodies, we can say that, q₁ + q₂ + q₃ +…..+ q_n = constant

Practical Application of Principle of Conservation of Momentum Vector:

When a bullet is fired from the gun, the gun recoils or gives a jerk in the shoulder in the backward direction. Let M be the mass of gun and m be the mass of the bullet. Initially both bullet and the gun are at rest. On firing the gun, suppose that the bullet moves with velocity v and the gun moves with velocity V. As we use the principle of conservation of momentum,
Total momentum of the gun and the bullet before firing = total momentum of the
         bullet and the gun after firing
0 = MV + mv
V = - mv / M
The negative sign shows that the gun will move in the opposite direction of bullet.