Visualization of the rolling motion of spheres connected with a rubber band using an image processing technique

Abstract

The traditional physics laboratory has adopted a photogate and polarized light to measure rotation motion in a fixed system, but they are not applicable to rolling objects. Computer vision has played an increasingly important role in image analysis. The popularization of mobile phones, cameras and computers makes it possible to measure the rotation of an object in a simple but nonintrusive way in a physics laboratory. A ‘tracker’ has been used to analyze the rotation motion of large objects, such as vehicle wheels, by recognizing the position of a marker. However, it is still challenging to precisely recognize the marker in a small object via simple algorithms in a physics laboratory. In this paper, we introduce a facile image processing technique to visualize the rotation and spin motion of spheres by marking it with two red and green semi-spheres. A basic formula of projection was derived to analyze the expression of spin angles with the projection area of the semi-sphere. The precision and suitability of the image processing technique was proven to be effective through comparison with the photogate measurement technique. The image processing technique has also been used to analyze the rotation and spin motion of two spheres bonded with a rubber band. It provides not only the trajectory of sphere centers, but the evolution of spin angles, orbit diameter and orbit angles of spheres. By analyzing the relationship between spin angles and orbit diameter, it is clear that the rubber band experienced typical transformations between three different phases (twist, coil and supercoil) until the energy was exhausted. The method offers valuable insights into rotational dynamics, showcasing its potential for practical applications in the physics laboratory and in educational contexts.