STUDY OF THE MOVEMENT OF A MATERIAL PARTICLE ON A FLAT DISK ROTATING AROUND A PERPENDICULAR AXIS INCLINED TO THE HORIZON

Abstract

The movement of material particles along rotational planes is complex, since it should be considered as the result of the movement of the plane itself and the particle along this plane. The task becomes more difficult if the moving plane is inclined at a certain angle to the horizon. Its solution makes it possible to find out the regularities of the movement of a particle along an inclined plane, which rotates around an axis perpendicular to it. The purpose of the study is to establish the patterns of movement of material particles on a flat disc with and without blades, which rotates around a perpendicular axis inclined to the horizon. If a round disk rotating around an axis perpendicular to it is located horizontally, then the kinematic parameters of the particle's motion on it do not depend on the point of impact of the particle on the disk. If the disk is tilted at a certain angle β to the horizon, it is obvious that the absolute trajectories of the particle's movement and other parameters of the movement will not be the same and will depend on the sector of the disk from which the particle starts its movement. The relative and absolute motion of a particle on an inclined disk with and without rectilinear blades is considered. A system of differential equations of particle motion has been compiled using the accompanying trihedron of the transfer trajectory, which is a circle, and Frenet's formulas. Numerical integration of the system was carried out. The obtained results were visualized. It was established that when particles hit an inclined disk that rotates around its own axis, the absolute trajectories of motion differ significantly from the trajectories of motion along a horizontal disk, and the difference in trajectories increases with an increase in the angle of inclination β. If rectilinear vanes are installed on the disc in the radial direction, the difference between the particle motion parameters will increase insignificantly as the angle β increases. When increasing the angular speed of rotation of the disk at a given angle, the shape of the absolute trajectories of particle motion practically does not change, but they are different depending on the point of impact on the disk. There is a certain area of impact and a certain sector of trajectories, after passing which the particle flies up after leaving the disc. Among this set, it is possible to analytically find the point of impact and the corresponding trajectory, which provide the maximum angle of elevation of the particle (equal to the angle β).