The Angular Speed Distribution of Randomly Moving Particles

Spin is a common phenomenon in nature, but the detailed statistical principle behind it is seldom discussed. This article aims to inspire people to think about such problems. In this article, probability theory and the corresponding modules of Mathematica software are used to study the distribution of angular speed generated by a population of equal speed particles moving randomly in space. The probability density expression of this distribution is derived successfully, and then its accuracy is verified by simulation data. Finally, it is confirmed that the angular speed follows the Maxwell distribution with a specified scale parameter. This research may be helpful for understanding why most celestial bodies or micro particles in the universe spin.