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Angular momentum

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The angular momentum is a property that has a mass that is in motion about a given axis , in a closed domain is retained. When we talk about the atmosphere, the angular momentum is a quite useful parameter to achieve studies of the dynamics at different scales, whether they are temporal or spatial . When the reference axis is identified with that of the figure of the Earth, which we can call the principal axis , the value of the resulting globally integrated axial angular momentum can also be treated as a fundamental index of theatmospheric circulation . As such, this parameter reflects many aspects of the signing of the climate and weather .

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  • Unit:  Kg m 2 / s
  • Formula:  P = mv

What is angular momentum?

Angular momentum is a vector quantity that is responsible for indicating the state of rotation that bodies have around a certain point and is part of classical , quantum and relativistic mechanics .

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  • Definition
  • Angular momentum of a particle
  • Angular moment of a rigid body
  • Orbital angular momentum
  • Conservation
  • Relationship to torque
  • Examples

Definition

It is one of the most important magnitudes in the area of physics . It is defined as the amount of movement that is associated with an object that performs a rotation around a certain point or a fixed point . Angular motion can occur around the object’s own center of mass and for this reason, when looking for angular momentum, it is also important to know the moment of inertia that a body possesses.

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When we refer to the angular momentum of the earth , we say that it is the sum of its angular momentum on its own axis around an imaginary axis that is located at the center of mass of the Earth-Sun system.  The angular momentum is a quantity that is always conserved, it is the sum of the angular momentum that is transferred from one body to another within a closed system that will always be zero, for this reason, the amount of energy that is transferred to another body will always be it will be equal to the amount that is received by other bodies.

Angular momentum of a particle

The angular momentum of a particle can be defined as the vector product of the position vector r by the vector time linear mv . It must be measured in SI in Kg m 2 / s.  This can be represented by the formula:

P = mv

Where m is the mass and v is the speed of the particle. This equation can also be rewritten as L = mrxv . The letter L refers to the perpendicular vector magnitude ar and a v. X refers to the angle between r and v . Every time r and v are parallel to each other, it tells us that the particle’s angular momentum is zero.

Angular moment of a rigid body

The particles that we find in a rigid solid that is in rotation around a fixed axis describe circles that are centered on the axis of rotation and that have a speed that is proportional to the radius of the circle that they describe:

i = wr i

The angular momentum possessed by rigid bodies is equal to:

The projection z of the angular momentum vector along the axis of rotation is:

Angular moment of a rigid body

Orbital angular momentum

When we talk about the orbital angular momentum, we refer to the angular momentum of the electrons that we find in the atoms , which are associated with a certain quantum state, and are quantized as follows:

Angular momentum, formula, orbital 2

Where l is the quantum angular momentum of the number and is also 0, 1, 2… n-1.

We can say that this is the result of applying quantum theory to the orbit that the electron possesses. The solution of the Schrödinger equation gives us the quantum number of the angular momentum.

Angular momentum, formula, orbital

Conservation

In the area of ​​physics we call by the name of the moment of a force about a point, the vector product of the position vector of the force and the force vector . Regarding the conservation of angular momentum, there is an important principle of conservation of angular momentum, which states that if the moment of the external forces is equal to zero (a situation that does not imply that the external forces are zero, that it is an isolated system ), the angular momentum as a whole is conserved, in other words, it remains constant . Its formula is the following:

dL / dt = M ext

ext = 0

L = cte

Relationship to torque

It is important to know that a torque is a measure of force that makes a certain object rotate around an axis. The torque is then responsible for making an object achieve an angular acceleration . It is a vector quantity and the direction of the torque vector depends on the direction of the force on the axis . Torque produces a variation or a change in the angular momentum of a group of particles or it can also occur in a rigid object .

Examples

An example would be a soda can that is rolling down a street that has a slope or also the wheel of a bicycle that keeps turning until it is stopped by something. In these two examples we can say that they have angular momentum.

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