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 isn't 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.
See also:
He Wonders Whether to Praise or to Blame Her
I have peace to weigh your worth, now all is over,
For, who decries the loved, decries the lover;
The more fool.html">fool.html">fool.html">fool.html">fool I, so great a fool to adore;
The more your godhead is, I lose the more.
Dear fool, pity the fool who thought you clever!
Most fair, -- the blind has lost your face for ever!
For, foul or lovely, 'twas a fool that loved you.
Softly along the dim way to your room,
And holiness about you as you slept.
About my head, and held it. I had rest
I knelt a long time, still; nor even wept.
It was great wrong you did me; and for gain
And sleepy mother-comfort!
How easily love.html">love leaps out to dreams like these,
Takes all too long to lay asleep again.
One Day
Today I have been happy. All the day
Its laughter with the dancing light o' the spray,
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Stray buds from that old dust of misery,
Just as a child, beneath the summer skies,
For which (he knows not) towns were fire of old,
And great kings turned to a little bitter mould.
Waikiki
Warm perfumes like a breath from vine and tree
Somewhere an `eukaleli' thrills and cries
And dark scents whisper; and dim waves creep to me,
And new stars burn into the ancient skies,
And still remember, a tale I have heard, or known,
Of two that loved -- or did not love -- and one
A long while since, and by some other sea.
Hauntings
In the grey tumult of these after years
And less-than-echoes of remembered tears
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