# Giroscopo

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Assignment: Instrumentation
Project: Gyroscope
Objective
* To make a gyroscope and make an application of the gyroscope using one of its properties, the rigidity and the precession, chose one of the properties and make and application of the gyroscope that we create.
Theory
A gyroscope is a device for measuring or maintaining orientation, based on the principles of conservation ofangular momentum. In essence, a mechanical gyroscope is a spinning wheel or disk whose axle is free to take any orientation. This orientation changes much less in response to a given external torque than it would without the large angular momentum associated with the gyroscope's high rate of spin.
A gyroscope has three axes. First, a spin axis, which defines the gyroscope strength or moment. Let uscall the other two the primary axis and the secondary axis. These three axis are orthogonal to each other.
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The spin axis rotates around the vertical line. The primary axis rotates the whole gyroscope in the plane of the page, and the secondary axis rotates the gyroscope up-and-over into the page.
The spin axis is the source of the gyroscopic effect. The primary axis is conceptually the inputor driving axis, and the secondary the output. Then if the gyroscope is spun on its spin axis, and a torque is applied to the primary axis, the secondary axis will precess. The primary axis appears infinitely stiff to the applied torque and does not give under it. This is the generally recognised characteristic of gyroscopic behaviour.
It is important not to confuse the concepts of angularmomentum and gyroscopic moment. When a mass ‘m’ moves in a straight line at velocity ‘v’ it exhibits linear momentum (m.v ). It is trivial to predict that if it is constrained to travel in a radius ‘r’ it will produce an angular momentum (m.v.r). However with the angular momentum an effect that could not have been predicted turns up - gyroscopic behaviour. The fact that in the larger world the twoeffects occur together and in simple proportion to each other does not mean that this is always the case - gyroscopic behaviour occurs without angular momentum in electron behaviour, even though the terms ‘spin’ and ‘spin angular momentum’ are still used for historical reasons, even though there is no direct evidence that the electron’s mass or charge spins on its own axis. It may simply be thatrotating an object exposes the gyroscopic moments of the elementary particles that make it up, possibly through the asymmetric relativistic effects created by the centripetal acceleration; some major experimental work is required in this area.
Angular momentum has the form “kilogram-meters2 per second”. Gyroscopic moment has the form “Newton-meters per Hertz”, or torque required to produce aprecession rate of one Hertz. For those familiar with dimensional analysis, both have the dimensions ‘L2M/T’, which means only that they are related by a simple scalar number. However (as far as the author has been able to determine) the actual value has never been researched; it may be unity, it may not. Whatever the case, from here on I will ignore angular momentum and consider only the gyroscopicmoment, regardless of how it is generated.
The strength of a gyroscopic effect is termed the gyroscopic moment. I use the symbol ‘G’, in units “Newton-meters/Hertz”. A higher moment requires more torque to precess at the same frequency, or for the same torque precesses at a lower rate
Where a gyroscope receives torque on the primary axis and precession on the secondary, no work is being done. Thetorque ‘TP’ on the primary axis has no precession associated with it, while the precession rate ‘vS’ on the secondary axis is...
vS = TP / G
and has no torque associated with it. Since the rate of doing work on each axis is the torque times the precession on that axis, it follows that in this simple case no energy is involved.
Gyroscopes do not differentiate between primary and secondary axes -...