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Gyroscope

A gyroscope is a device which demonstrates the principle of conservation of angular momentum, in physics.

The essence of the device is a spinning wheel on an axle. The device once spinning tends to resist changes to its orientation. The gyroscope was invented and named in 1852 by Léon Foucault for an experiment involving the rotation of the Earth.

A gyroscope exhibits a number of behaviours including precession. Gyroscopes can be used to construct gyrocompasses which replace magnetic compasses (in aircraft and spacecraft), to assist in stability (bicycle, Hubble space telescope), as a repository for angular momentum (momentum wheels) and as a means to conserve and deliver energy (flywheel energy storage) in some machines. The flywheel in an engine is one such use. Gyroscopic effects are used in many different toys like for example yo-yos and dynabees.

The fundamental equation describing the behaviour of the gyroscope is:

<math>\mathbf{\tau}={{d \mathbf{L}}\over {dt}}={{d(I\mathbf{\omega})} \over {dt}}=I\mathbf{\alpha}</math>

where the vectors τ and L are the torque on the gyroscope and its angular momentum, the scalar I is its moment of inertia, the vector ω is its angular velocity, and the vector α is its angular acceleration.

It follows from this that a torque τ applied perpendicular to the axis of rotation, and therefore perpendicular to L, results in a motion perpendicular to both τ and L. This motion is called precession. The angular velocity of precession ΩP is given by

<math>\mathbf{\tau}={\Omega}_P \times \mathbf{L}</math>

Precession can be demonstrated by placing a spinning gyroscope with its axis horizontal and supported loosely at one end. Instead of falling, as might be expected, the gyroscope appears to defy gravity by remaining with its axis horizontal, even though one end of the axis is unsupported. The free end of the axis slowly describes a circle in a horizontal plane. This effect is explained by the above equations. The torque on the gyroscope is supplied by a couple of forces: gravity acting downwards on the device's centre of mass, and an equal force acting upwards to support one end of the device. The motion resulting from this torque is not downwards, as might be intuitively expected, causing the device to fall, but perpendicular to both the gravitational torque (downwards) and the axis of rotation (outwards from the point of support), i.e. in a forward horizontal direction, causing the device to rotate slowly about the supporting point.

As the second equation shows, under a constant torque due to gravity, the gyroscope's speed of precession is inversely proportional to its angular momentum. This means that, as friction causes the gyroscope's spin to slow down, the rate of precession increases. This continues until the device is unable to rotate fast enough to support its own weight, when it stops precessing and falls off its support.

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