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 the**atmospheric circulation** . As such, this parameter reflects many aspects of the signing of the **climate** and **weather** .

**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** .

- 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.

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:

**V _{i} = wr _{i}**

The angular momentum possessed by rigid bodies is equal to:

The **projection ****L _{z}** of the angular momentum vector along the axis of rotation is:

## 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:

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.

## 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}**

**M _{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.