The problem of the body rotating on a frictionless table, attached to a hanging body, solved partially by conservation theorems

Abstract

Conservation theorems of Mechanics, have been applied to the problem consisting of a body rotating on a frictionless table, attached to a hanging body, as an illustrative example for students of Physics with no knowledge of sophisticated mathematical methods, how to obtain a description of the physical behavior of a system, when obtaining the equation of motion requires those complicated methods. Applying the conservation of angular momentum it is shown that the angular frequency increases inversely to the square of the radius of motion; then the radius  is found at which the centripetal force and the tension of the string compensate each other; then, applying the conservation of energy, turning points are found. At the end, following scenery is obtained: the radial component of motion of the rotating body takes place between two turning points, namely a maximum at  given by the initial conditions, and a minimum at . With the help of these equations, obtained without the need of solving differential equations, it is possible to obtain a semi quantitative physical behavior of this particular system.