# Momentum: conservation law, classical mechanics

The **momentum or linear momentum** , also known as momentum, is defined as a physical quantity in the vector type classification, which describes the movement that a body performs in mechanical theory. There are several types of mechanics that are defined in amount of movement or momentum.

Classical mechanics is one of these types of mechanics and can be defined as the product of body mass and speed of movement at a given moment. Relativistic mechanics and quantum mechanics are also part of linear momentum.

There are several formulations about the amount of movement. For example, Newtonian mechanics defines it as the product of mass and velocity, while in Lagrangian mechanics the use of self-connected operators defined in a vector space in an infinite dimension is necessary.

Momentum is governed by a law of conservation, which states that the total momentum of any closed system cannot be changed and will always remain constant over time.

__Law of conservation of momentum__

__Law of conservation of momentum__

In general terms, the law of conservation of momentum or momentum expresses that when a body is at rest, it is easier to associate inertia with mass.

Thanks to mass, we get the magnitude that will allow us to rest a body and, in case the body is already in motion, the mass will be a determining factor when changing the velocity direction.

This means that depending on the amount of linear motion, the inertia of a body will depend on its mass and velocity.

The equation of momentum expresses that momentum corresponds to the product of mass and velocity of the body.

p = mv

In this expression, p is the momentum, m is the mass, and v is the velocity.

__classical mechanics__

__classical mechanics__

Classical mechanics studies the laws of behavior of macroscopic bodies at speeds much slower than those of light. This momentum mechanic is divided into three types:

**Newtonian Mechanics**

Newtonian mechanics, named after Isaac Newton, is a formula that studies the motion of particles and solids in three-dimensional space. This theory is subdivided into static mechanics, kinematic mechanics and dynamic mechanics.

Statics deals with the forces employed in a mechanical balance, kinematics studies motion without taking into account its result, and mechanics studies motion and its results.

Newtonian mechanics is primarily used to describe phenomena that occur at a speed much slower than the speed of light and on a macroscopic scale.

**Langgian and Hamiltonian mechanics**

Langrian mechanics and Hamiltonian mechanics are very similar. Langgian mechanics is very general; for this reason, its equations are invariant with respect to some changes that occur in the coordinates.

This mechanics provides a system of a number of differential equations known as equations of motion, from which one can infer how the system will evolve.

On the other hand, Hamiltonian mechanics represents the momentary evolution of any system through first-order differential equations. This process makes equations much easier to integrate.

**Continuous Media Mechanics**

Continuous media mechanics is used to provide a mathematical model on which you can describe the behavior of any material.

Continuous means are used when we want to find out the amount of movement of a fluid; In this case, the momentum of each particle is added up.

__Relativistic Mechanics__

__Relativistic Mechanics__

Relativistic momentum mechanics – also following Newton’s laws – states that since time and space exist outside any physical object, Galilean invariance occurs.

For his part, Einstein maintains that the postulation of the equations does not depend on a frame of reference, but accepts that the speed of light is invariant.

At present, relativistic mechanics works in a similar way to classical mechanics. This means that this magnitude is greater when referring to large masses, which move at very high speeds.

In turn, it indicates that a large object cannot reach the speed of light, because eventually its momentum would be infinite, which would be an irrational value.

__quantum mechanics__

__quantum mechanics__

Quantum mechanics is defined as a hinge operator on a wave function and that follows the Heinsenberg uncertainty principle.

This principle sets limits on the timing precision and position of the observable system, and both can be discovered at the same time.

Quantum mechanics uses relativistic elements when addressing various problems; This process is known as relativistic quantum mechanics.

__Relationship between moment and amount of movement__

__Relationship between moment and amount of movement__

As mentioned earlier, momentum is the product of velocity and object’s mass. In the same field, there is a phenomenon known as momentum, which is often confused with momentum.

The impulse is the product of the force and the time during which the force is applied and is characterized as a vector magnitude.

The main relationship that exists between impulse and amount of motion is that the impulse applied to a body is equal to the variation of the moment.

In turn, as impulse is the product of force over time, a certain force applied at a certain time causes a change in momentum (regardless of the object’s mass).

__Amount of Movement Exercise__

__Amount of Movement Exercise__

A baseball with 0.15 kg of mass is moving at a speed of 40 m / s when it is hit by a bat that reverses its direction, acquiring a velocity of 60 m / s, with what average force the bat exerted the ball if it was in contact with these 5 ms?

**Solution**

**Data**

m = 0.15 kg

vi = 40 m / s

vf = – 60 m / s (sign is negative as direction changes)

t = 5 ms = 0.005 s

Δp = I

mp – pi = I

m.vf – m.vi = Ft

F = m. (Vf – vi) / t

F = 0.15 kg. (- 60 m / s – 40 m / s) / 0.005 s

F = 0.15 kg. (- 100 m / s) / 0.005 s

F = – 3000 N