The angular speed distribution of randomly moving-particle group

Rotation is a common phenomenon in nature, although 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 speeds generated by a population of equal-speed particles moving randomly in space. The probability density expression of this distribution is derived successfully, and its accuracy is then verified using simulation data. Finally, it is confirmed that the angular speed follows a Maxwell distribution with a specified scale parameter. This research may be helpful for understanding why most celestial bodies or microparticles in the universe are in rotation.