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## The Gyroscope Forum

25 March 2019 21:09

Welcome to the gyroscope forum. If you have a question about gyroscopes in general, want to know how they work, or what they can be used for then you can leave your question here for others to answer. You may also be able to help others by answering some of the questions on the site.

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### Question

Asked by: Colin White
Subject: Magnitude of precession
Question: The period of precession of a gyroscope is well documented and a simple formula characterises it. But, what about the magnitude of precession angle. The precession angle must be governed by the period of rotation, the moment of inertiaand how hard it is knocked from the alignment with the gravity vector. But is there a formula that will provide this value for the size of the precessing gyroscope?
Thank you

Colin
Date: 15 August 2008
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### Answers (Ordered by Date)

Answer: PATRICK - 16/12/2008 22:42:20
COLIN

My email neither works or do i read but if u read any input of mine in the forum pls try pythagoras in all decimal points,I myself like 8. 367 inner 359 OUTER incraments.
Draw a line from 1 outer to another passing through the inner.....YET do not touch the eppicentre,pass by but count passes and only work in oyher than decimal 10 ie 7 or 8 recording each rebound from the outer in both their incramental degrees

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Answer: Albert Keel - 03/01/2009 23:54:15
Hello!

THANKS!

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Answer: Petruchio - 24/06/2009 04:59:05
The answer to this question is well known. Gyros are normally like tops, pivotted quite close to the c.g. For any gyro there are two modes of precession, the high and low speed cases. The precssion rate, P, in rads/sec for the hight speed case is given by: Pcos(t) = Cn/A where t is the tilt angle of the axle from the vertical, C the moment of inertia about the axle, and A the moment of inertia about the pivot and n the angualr velocity about the axle. The slow precession is given by: P =mgl/Cn) ,where m is the mass, g, accel. due to gravity, l height c.g. above pivot (positive for a normal top) . Curiously the slow precession is not a function of the tilt angle. The above expressions are exact.

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Answer: pierre Jones-Savard - 10/01/2010 14:28:05
Salute, i foun it and here the formula:

O = 2[(variability angle)/(180 degres)]E , (equation 1),

O is the periode of precession angle,
(variability angle) is variability of the gyroscope axis angle,
E is periode of precession, for 360 degrees.

Example: for Earth equinox precession is about 26 000 years and (variability angle) is about 2.4 degrees, then from equation 1, O = 693 years about,

on the web, Milancovitch cycle of 41 000 years is not truth for the variability angle of Earth axis of about 2.4 degrees and a write this in a French forum.
I try to find a web page, instead of mine that proof that equation 1 is truth.
here my web page for the precession angle, (equation 19)/(equation 20) is good, here the web page in French:
http://www3.sympatico.ca/pierrejsavard/le_cycle_de_la_variabilite_de_l_axe_de_la_terre_est_de_693_ans3.pdf

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