Visualizing the rolling motion of spheres connected with rubber band by imaging processing technique

Traditional physics laboratory adopted photogate and polarized light to measure the rotation motion in a fixed system, but they are not applicable to the rolling objects. Computer vision has played increasing 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 physics lab. "Tracker" has been used to analyze the rotation motion of large object, such as vehicle wheels, through recognizing the position of marker. However, it is still challenging to precise recognize the marker in small object via simple algorithms in physics lab. In this paper, we introduced a facile image processing technique to visualize the rotation and spin motion of spheres through marking it with two red- and green- semi-spheres. The basic formula of projection was derived to analyze the expression of spin angles with projection area of semisphere. The precision and suitability of the image processing technique was proved to be effective through comparison with the photogate-measure technique. The image processing technique has also been used to analyze the rotation and spin motion of two spheres bonded with rubber band. It provides not only the trajectory of sphere centers, but the evolution of spin angle, orbit diameter and orbit angle 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, helix and superhelix, until the energy was exhausted. The method offers valuable insights into rotational dynamics, showcasing its potential for practical applications in physics lab and educational contexts.