Angular Momentum and External Torque

h6. Gyroscopic Approximation 
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The *gyroscopic approximation* assumes that the angular momentum due to precession of the gyroscope is negligible compared to the angular momentum of the spinning gyroscope. If Ω is the angular velocity of precession and ω is the angular velocity of the gyroscope's spin, then the gyroscopic approximation holds when

{latex}\begin{large}\[ \Omega \ll \omega \]\end{large}{latex}
and 
{latex}\begin{large}\[ \vec{L} \simeq \vec{\omega} I\]\end{large}{latex}

_I_ is the moment of inertia of the gyroscope about the spin axis {latex}$\hat{\omega}${latex}
See [Spinning Top]  and [Delta-v diagram] for more details.
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h6. Angular Frequency of Gyroscopic Precession
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Under the gyroscopic approximation, the angular velocity of the precession is given by Ω 

{latex}\begin{large}\[\displaystyle  \Omega = \frac{\displaystyle \left(\frac{dL}{dt}\right)}{L} \]\end{large}{latex}

This result is independent of the tipping angle of the gyroscope.

h6. Differential Form
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{latex}\begin{large}\[\sum_{\rm system}\frac{d\vec{L}}{dt} = \sum_{\rm external}\vec{\tau}\]\end{large}{latex}
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