# Angular momentum

## Contents

## Explanation[edit]

In classical mechanics, the angular momentum is the rotational momentum of an object that is rotating about an axis. The object can also have spin angular momentum if it is spinning about its own axis. For an object orbiting around an axis, the angular momentum is mathematically described as a cross product of the object's position vector **r** and the linear momentum vector **p**. It is also described as the product of the angular velocity **ω** and moment of inertia **I**. In all the cases, when there is no external torque acting on the object, the angular momentum is conserved. For example, our Earth spins on its own axis as it revolves around the Sun in an orbit. In this case, the earth has both a rotational angular momentum and a spin angular momentum.

## Frequently Asked Questions[edit]

### How is the direction of angular momentum determined?[edit]

Angular momentum is a pseudovector that has an arbitrary direction pointed in the direction of the rotation or spin. When an object, say a ball, is spinning about an axis clockwise, it is impossible to determine the direction of a point on the surface of the ball. The direction changes at each instant as the ball spins. So mathematically, applying the cross product for angular momentum calculation a pseudovector can be determined in three dimensions. This can also be set using the right-hand rule, where you curl up your right hand in the direction of the rotation. The direction of the thumb would be the direction of the angular momentum pseudovector.

### Why is angular momentum studied in quantum mechanics?[edit]

Studying the behaviour of electrons around a nucleus is a vital part of quantum mechanics. As electrons are found in discrete orbitals when in a bound state, they have a certain orbital angular momentum. Besides this, electrons also have an arbitrary spin angular momentum. So by studying the angular momentum of particles, quantum mechanics can be understood better.

### How is angular momentum conserved?[edit]

Just like in linear systems, where the linear momentum is conserved as long as no external forces act on it, in rotational systems, the angular momentum is conserved as long as no external torques acting on it. For example, the orbital angular momentum of the Earth and other planets in the solar system are conserved. This is the reason why all planets revolve around the sun in the same plane and same anti-clockwise direction. As long as no planetoids or asteroids hit them, they will continue to do that forever.