# Gyroscope

A gyroscope (of the Greek “which looks at rotation”) is an apparatus which exploits the principle of the conservation of the Angular momentum in Physique (or gyroscopic stability or gyroscopic effect). In the sensors: a gyroscope is an angular position transducer and a Gyromètre an angular velocity pick-up. The gyroscope gives the angular position (according to one, two or the three axes) of its reference frame compared to a inertial Référentiel (or galiléen).

### Gyroscopic effect

The essence of the device is a wheel (or any correctly balanced object) turning on an axis which, once launched tends to resist the changes of its orientation.

The simplest demonstration and more speaking consist in holding with end of arm a wheel of bicycle by the nuts of the hub and to make it turn quickly by another person. When one tries to lean on the side the wheel in rotation, one feels a resistance. It is the conservation of the turning moment which tends to be opposed to this movement.

## The gyroscope of Foucault

The gyroscope was invented and named in 1852 by Leon Foucault for an experimentation implying the rotation of the Earth. Rotation had already been highlighted by the Pendule of Foucault. However Foucault still did not include/understand why the Rotation of the pendulum was carried out more slowly than the rotation of the ground (of a factor $\left\{1\right\} \ over \ sin \left(\left\{latitude\right\}\right)$).

Another instrument was thus necessary to highlight the rotation of the simple Earth of way. Foucault thus presented in 1852 an apparatus able to preserve a sufficiently fast rotation (150 to 200 rotations a second) and during long enough (ten minutes) so that observable measurements can be carried out. This mechanical prowess (for the time) illustrates the talent in mechanics of Foucault and his collaborator, Froment.

Foucault realized also that its apparatus could be used to indicate the Northern . Indeed, by blocking certain parts, the gyroscope is aligned on the Méridien. The gyroscopic compass had been born.

## General information

The operation of the gyroscope rests on the phenomenon of Précession.

The gyroscopes can be used to build gyroscopic compasses which complémentent or replace the magnetic compasses - in the ships, aircraft and vehicles in general - like helping with the stability of the bicycles, of the Space telescope Hubble and like a deposit for the moment angular for the inertial wheels.

The gyroscopic effects are also the base of toys like the Yo-yo S, Powerball S and the Toupie S.

## Physical laws

The fundamental equation describing the behavior of the gyroscope is:

$\vec\tau===I\vec \alpha$

where the vectors $\ vec \ tau$ and $\ vec L$ are respectively the moment on the gyroscope and its kinetic moment, the scalar I is its moment of inertia, the vector $\ vec \ omega$ is its angular velocity, and the vector $\ vec \ alpha$ is its angular acceleration.

It rises from that one moment $\ vec \ tau$ perpendicular applied to the axis of rotation, and thus perpendicular to $\ vec L$, causes a displacement perpendicular at the same time to $\ vec \ tau$ and $\ vec L$. This movement is called precession . The angular velocity of the ΩP precession is given by

$\ vec \ tau= \left\{\ Omega\right\} _P \ vec L$

The phenomenon of precession can be observed while placing a gyroscope turning on its axis horizontal and supported loosely at an end. Instead of falling as one can expect it, the gyroscope seems defying gravity while remaining on his horizontal axis, even if an end of the axis is not supported. The loose lead of the axis slowly describes a circle in a horizontal plane. This effect is explained by the preceding equations. The moment of the gyroscope is provided by a couple: gravity pushes to the bottom the center of mass of the device, and a force equalizes the growth upwards to support the free side. Displacement resulting from this moment is not to the bottom, like the intuition makes us suppose it, but perpendicular at the same time to the gravitational movement (bottom) and it axis of rotation (towards the outside of the fulcrum), i.e. in a horizontal direction forwards, making make with the apparatus a slow rotation around the point of support.

As the second equation shows, under one constant moment due to gravity, the speed of precession of the gyroscope is inversely proportional to its kinetic moment. That means that, like the friction makes slow down the turning movement of the gyroscope, the rate of precession increases. That continues until the device cannot turn any more sufficiently quickly to support its own weight, then it stops the precession and fall out of its support.

## Uses

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