THE MOTION OF A PARTICLE ON A HORIZONTAL CYLINDER THAT ROTATES AROUND ITS OWN AXIS
Abstract
Cylindrical surfaces are an integral part of agricultural machinery. In hoisting and transport machines, cylindrical surface is a casing, inside which the working body rotates. The interaction of particles with the surface of the cylinder, which rotates around its own axis, leads to their sliding, the nature of which depends on the angle of the cylinder. The article investigates the motion of a particle on the inner surface of a horizontal cylinder that rotates around its axis with a constant angular velocity. It is clear that the motion of an individual particle cannot be identified with the motion of a material consisting of individual particles, but it makes possible to determine the laws of motion that can be in some way transferred to the material. In addition, the study of body motion in some cases can be reduced to a particle. This applies to the case when the forces of inertia from the rotation of the body can be neglected due to the small angular velocities of their rotation. When a particle hits the inner surface of a horizontal cylinder that rotates with an angular velocity ω around its own axis, it begins to oscillate in the cross-sectional plane of the cylinder with a certain amplitude in the angular dimension. The value of the amplitude depends on the point of impact of the particle, the coefficient of friction and the initial absolute velocity. Differential equations of motion are compiled in projections on the axis of a fixed coordinate system and are solved by numerical methods. Under the appropriate initial conditions, which are determined analytically, the particle in absolute motion can be stationary, being at a point on the cylinder at a certain distance from the lowest point in the angular dimension during the rotation of the cylinder. The value of the angular velocity has great importance. When it reaches a certain value, the particle practically “sticks”.
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