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Is spin angular momentum increasing in a gyroscope?

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In my textbook there is an equation for the precession frequency:

Ω = τ/Iω

The derivation in the book shows no difference in the spin angular momentum at time t = 0 and t = delta t but when I tried it I got that the denominator of the above equation must be the 'new' angular momentum (at t = delta t)

If the spin angular momentum is increasing with time wouldn't that means the precession frequency would be decreasing but my textbook says constant velocity

:confused:

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