newtonian mechanics - Why does a Yo-Yo sleep, and then awaken?

What are the mathematics / mechanics principles behind a sleeping Yo-Yo, and in particular, what changes with a wrist-snap flick that causes it to "awaken" and return to your hand?

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            ^{(Image from www.wikihow.com/Make-a-Yoyo-Sleep.)}

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There must be some stability principle that keeps it asleep, and which is disturbed by the tug.

Answer

If the yoyo is spinning without winding the string, then it must be that the friction between the inner barrel and the string is insufficient to lead to winding.

A flick of the wrist or some other movement can lead to an increase in the friction and the beginning of winding.

Once winding begins frictional forces between the string and barrel increase with more string in close contact with the barrel and wound string overlaying earlier wound layers. Hence it is rare for the string to slip after that process has begun.