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?

            (Image from www.wikihow.com/Make-a-Yoyo-Sleep.)
There must be some stability principle that keeps it asleep, and which is disturbed by the tug.

  • 4
    $\begingroup$ Ever open one up? $\endgroup$
    – Kyle Kanos
    Jun 13, 2015 at 23:50
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    $\begingroup$ @KyleKanos: When I was a child, YoYos were two circular blocks of wood connected by a metal rod. They slept and awakened just fine. It is not internal structure that is primarily responsible. $\endgroup$ Jun 13, 2015 at 23:52
  • 1
    $\begingroup$ When I was a kid, they were made of plastic, a metal axle, and a bearing. The axle was threaded onto the plastic ends, hence opening one up. $\endgroup$
    – Kyle Kanos
    Jun 14, 2015 at 0:43
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    $\begingroup$ When I was a kid, they were two wooden disks with a wooden dowel as a fixed axle. The glue made it rather difficult to open one up. They slept just fine unless the string was twisted (not wound) too tightly, and there was plenty of time to do cradles and such. $\endgroup$ Jun 14, 2015 at 3:58
  • $\begingroup$ I appreciate the knowledgeable (and cordial) responses & comments by several, and I have accepted SimonS's answer, particularly in light of LDC3's clarifications. However, I do think the exact sequence of events that occur with a flick that awakens the Yo-Yo bears further scrutiny. Perhaps that is a separate question. I do not think merely an increase in tension/friction explains it. Also the following sudden decrease is important, and likely the dynamics are complex. $\endgroup$ Jun 15, 2015 at 23:14

3 Answers 3


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.

  • 2
    $\begingroup$ If the Yo-Yo precesses, then the rubbing of the string by the side is sufficient friction to get the Yo-Yo to wind up the string. When you flick your wrist, the tension on the string is removed and the friction of the metal shaft is sufficient to wind the string. $\endgroup$
    – LDC3
    Jun 13, 2015 at 23:56
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    $\begingroup$ @JosephO'Rourke An upwards flick would temperately increase the friction with the string, then the friction would decrease dramatically when the tension is released. $\endgroup$
    – LDC3
    Jun 14, 2015 at 13:36
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    $\begingroup$ Yes, but that would be hard to do since it would necessitate that the hand accelerate constantly (like gravity). $\endgroup$
    – LDC3
    Jun 14, 2015 at 14:50
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    $\begingroup$ My intuition is that a gradual increase in tension would not initiate a reeling-in, but rather the sudden increase followed by sudden decrease in tension is somehow crucial---in other words, the flick is essential. So I feel there is a lacuna in the explanation, but maybe if no one else is left uneasy... $\endgroup$ Jun 14, 2015 at 23:12
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    $\begingroup$ The slack in the string will allow the yo-yo to wind the string. Once there is one winding around the spindle, it becomes tight and increases friction a lot. $\endgroup$
    – LDC3
    Jun 14, 2015 at 23:48

Its really a great question and let us go by simple definition.


As per what wikepedia says:

A yo-yo (also spelled yoyo) is a toy which in its simplest form is an object consisting of an axle connected to two disks, and a length of string looped around the axle, similar to a slender spool.


But what really makes it work? In simple it is energy converting machine. If we see at first yo yo has some potential energy as it is above the ground. But when we release yo yo. It converts that potential energy to kinetic energy. When a yo yo spins at bottom generally its the kinetic energy of rotation. enter image description here

In general we can say that yo yo can spin up and down forever but what makes it stop is :

string is attached with plastic axle therefore there is friction force acting between two objects.

And the air resistance as yoyo wheels also rub air which we are not able to see.

The image of simple yoyo when it is opened:

enter image description here


It is simply solved as I am no expert. Diagram below this:

$$-mg+T=ma$$ $$\tau=I \alpha ,Tr = I \alpha$$ $$v=-r \omega , a=-r \alpha $$

From 2 and 3

$$a= -\frac{g}{1+I/mr^2}$$

$$I = \frac{1}{2} m R^2$$

$$a=- \frac{g}{1+ \frac{1}{2}(R/r)^2}$$

enter image description here

There are clutch yoyo which acts quite interesting which acts because of centrifugal force and they call them centrifugal clutch. What makes this yoyo different is that there is one spring mechanism attached inside the yoyo. Whenever the yoyo is rotating slowly then springs comes contact with the axle and makes it fall back on the string. But the main advantage is that if the yoyo is rotating much faster, then the weights fly out from the axle (weights are attached with spring) because of centrifugal force. Now there is nothing to clamp and it is free to move at the bottom and when it got slow down then it come in contact with axle and got back up because of friction.

Here's the photo showing this mechanism :

enter image description here

Here at this image you will notice how clutch yoyo works. If you see when you spin hard those two solid bars go away but if you will flick it will come back automatically to you.

enter image description here


"Sleeping" is when the YoYo rotates in place because the string is freely rotating around the bar between the halves. If something is done to prevent the string from freely spinning then the energy that was driving the YoYo to rotate in place is now used to reel in the string. Flicking your wrist or otherwise jolting it can cause the string to double up on itself in the narrow gap between the halves, giving it enough friction to no longer freely spin around the bar and to instead begin spooling up. Note that this friction is usually not sufficient to prevent the YoYo from unraveling the doubled up string on its next trip down. The "sleeping" process can begin again when the string is again unraveled into the state where the loop can freely rotate around the bar in the middle, if the jolt of the YoYo reaching the end of its string isn't enough to cause the string to bunch up again as described above.

  • $\begingroup$ "the string to double up on itself": Nice explanatory phrase. $\endgroup$ Jun 14, 2015 at 11:15

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