In this paper, several more difficult problems are solved, the solutions of which are based on a fundamental law of classical dynamics: the law of conservation of angular momentum. The solutions to these problems are provided, and the results are analyzed in detail.The laws of conservation of momentum, angular momentum, kinetic energy, and mechanical energy form the theoretical basis of general and technical mechanics. This paper presents solutions to several more difficult problems in theoretical dynamics that utilize the law of conservation of angular momentum.
2. APPLICATION OF THE LAW OF CONSERVATION OF ANGULAR MOMENTUM IN COMPOUND MOTION
2.1 Example 1
Let there be a beam AB of length 2a and total mass m inside a thin cylinder fixed to the ground with radius R
2a
and a perfectly smooth inner surface. A material point, also of total mass m, is initially located at the center of the beam O at the intersection with the vertical diameter of the cylinder, as shown in Figure 1. At a certain moment, the material point m is given a constant horizontal velocity v relative to the beam in the direction of the end point of the beam
B . The beam begins to rotate during the movement of the point. It is necessary to determine the angle of rotation of the beam t as a function of time t .
According to the notation adopted in Figure 1, the angular momentum of the beam-material point system, calculated with respect to the center of the cylinder O, must be equal to zero. The mass moment of inertia of the system with respect to the center point of the cylinder (…)
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Source: Logistyka Magazine