The **key difference between spin and orbital angular momentum** is that spin angular momentum describes the angular momentum about the center of the object’s mass, whereas orbital angular momentum describes the angular momentum about a chosen center of rotation.

Angular momentum refers to the rotational analog of linear momentum. It is an important physical quantity since it is a conserved quantity that describes the total angular momentum of a closed system that stays constant. Generally, angular momentum has both direction and magnitude. It is also conserved. There are two specific types of angular momentum of an object: spin angular momentum and orbital angular momentum.

### CONTENTS

1. Overview and Key Difference

2. What is Spin Angular Momentum

3. What is Orbital Angular Momentum

4. Spin vs Orbital Angular Momentum in Tabular Form

5. Summary – Spin vs Orbital Angular Momentum

## What is Spin Angular Momentum?

Spin angular momentum is the velocity of rotation of something around a particular axis. Spin is sometimes known as angular momentum. It is the product of mass, velocity, and radius, where the radius is the distance between the spinning object and the axis. The SI unit for the measurement of spin angular momentum is Nms, Js, or Kgm2/s. Moreover, any change in the spin angular momentum of a system in which the total angular momentum is conserved is matched by an equal and opposite change in the orbital angular momentum of the same system.

## What is Orbital Angular Momentum?

Orbital angular momentum or the angular momentum of an orbital is the sum of the orbital angular momenta from each electron. Electrons in free space are able to carry quantized orbital angular momentum that is projected along the direction of propagation. This orbital angular momentum usually corresponds to helical wavefronts or equivalently phase proportional to the azimuthal angle.

Since angular momentum is a vector quantity, it represents the product of the rotational inertia of an object and rotational velocity, which is about a particular axis. In order to completely define orbital angular momentum in 3D, it’s important to know the rate of the position vector sweeping out angle, the direction that is perpendicular to the instantaneous plane of angular displacement, and also the mass that is involved. Moreover, the distribution of the mass in space is also required.

## What is the Difference Between Spin and Orbital Angular Momentum?

Spin and orbital angular momentum are related terms. The balance of angular momentum depends on the change of the spin or orbital angular momentum, which is canceled off by each other. The key difference between spin and orbital angular momentum is that spin angular momentum describes the angular momentum about the center of the object’s mass, whereas orbital angular momentum describes the angular momentum about a chosen center of rotation. Therefore, spin angular momentum is the motion of an object as it rotated around an axis through its center of mass, whereas orbital angular momentum is the motion relative to a point, often periodic, but not necessarily.

The following table summarizes the difference between spin and orbital angular momentum.

## Summary – Spin vs Orbital Angular Momentum

Spin angular momentum is the velocity of rotation of something around a particular axis, while orbital angular momentum or angular momentum of an orbital is the sum of the orbital angular momenta from each of the electrons. The key difference between spin and orbital angular momentum is that spin angular momentum describes the angular momentum about the center of the object’s mass, whereas orbital angular momentum describes the angular momentum about a chosen center of rotation.

##### Reference:

1. “Orbital Angular Momentum.” *Encyclopædia Britannica*, Encyclopædia Britannica, Inc.

2. “Angular momentum.” *Wikipedia*. Wikipedia Foundation.

##### Image Courtesy:

1. “Neutron spin dipole field” By Bdushaw – Own work (CC BY-SA 4.0) via Commons Wikimedia

2. “Laguerre-gauss modes larger text” By Tyharvey313 – Own work (CC BY-SA 4.0) via Commons Wikimedia

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