# Angular moment

Angular momentum is a physical quantity that measures the amount of motion of rotating bodies. It is one of the main quantities for the study of Rotational Kinematics.

Every body that is in motion has a property called momentum **(Q)** . However, when the body is performing a rotation movement, it will have **angular momentum** ( **L** ).

When in **rotation** , we say that the bodies present a momentum **related** to **the rotational motion ****,** the **angular **__ momentum__ .

Angular __ momentum__ is one of the basic properties of Rotational Mechanics and is closely related to the tendency of the body to continue its state of circular motion.

When the **speed ****of** the body is **perpendicular** (a 90º angle) to the direction of the axis of rotation, it is possible to calculate the **magnitude** of the angular momentum of the body with the following expression:

*L* = *r* . *Q*

Angular momentum is a **vector**** quantity** , therefore, it has **a** well – defined **magnitude** and **direction . **It is important to know that **angular momentum ****is** always **perpendicular** to the **plane** formed by **vectors ****r** and **Q** (distance from the axis of rotation and momentum, respectively).

Its unit of measurement in the International System of Units ( **SI** ) is **kg.m **^{2}** /s** , as it involves the product of a distance r (given in meters, **m** ) by a mass (in kilograms, **kg** ) and the velocity of the body **v** (in meters per second, **m/s** ).

Note in the figure below the spatial relationship between the three vectors **L** , **r** and **Q.**

In this figure, we can see an **orthogonal frame** of reference , with the **x** , **y** , and **z** directions represented. In the **xy plane,** the vectors **r** and **Q are shown. ****Perpendicular** to the plane formed by them, in the **z** direction , is the **angular momentum ****vector** , in green.

The quantity of motion is given by the product of the radius of rotation (r) and the **instantaneous ****velocity** of the body, so it is still possible to write the relationship of the **angular momentum ****as** a **function** of the **mass** and **speed** of the rotating body:

**L = r. m. v**

Many physical systems can be studied according to their amount of angular momentum, as one of the fundamental principles of physics says that: * “in the absence of any external forces, the amount of total angular momentum is maintained”. *In this way, it is possible to predict changes in the rotation speed of planets and other stars, as well as calculate the radii of their orbits and trajectories around their stars, etc.