Conical pendulum

The figure opposite represents a device called " pendulum conique". It is about a simple Pendule but which one attaches the end of the wire to a vertical axis of rotation (rigid stem driven by an engine).

If one makes start the engine slowly and that one increases the number of revolutions gradually, one observes that for a certain value, the pendulum deviates from the axis of a certain angle. The mass of the pendulum describes a circle then. The wire thus describes a cone, from where the name. The angle from which the pendulum deviates is all the more important as the number of revolutions is grande.

(It is noted that this is not with strictly speaking a pendulum since there is no oscillation).

This circular motion is explained by the combined effect of the weight and the tension of the wire which exerts a centripetal force maintaining the mass in rotation around the axis.

If m indicates the mass, L the length of the wire fixed out of O, and C the center of the circle describes by the mass, for a uniform angular velocity $\ omega_0$ , the half angle at the top $\ alpha$ is such as:

cos $\ alpha$ = g/l $\ omega_0^2$

History of sciences

Christiaan Huygens (1629-1695) will discover by studying this problem the acceleration of a uniform movement (which, let us recall it, was described by Galileo (1568-1642), like NOTHING). Huygens rectified a little by introducing the centrifugal force correctly, but will remain attached to the thought of Galileo, which will lead it to its unhappy theory of the total Relativité.

See too

simple Pendulum
Pendulum of spherical Huygens
Pendulum

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