What kind of physics are in yoyo?

# Physics

**frodoslair**#3

I donâ€™t know much about physics, but some things you could look into include:

Potential energy, kinetic energy, centrifugal force, gyroscopic stability, centripetal force, precession, inertia, effects of mass, speed, friction, etc. on a rotating object, and, I am sure there must be a ton more.

**TheRyanFace**#4

Yes, a yoyo is definitely a gyroscope.

But I think the most important physical concept involved is rotational inertia (things that are spinning at a certain angular velocity are going to want to stay that way). Thatâ€™s why when you play with a yoyo, it stays up-right in that direction. A yoyo tilts because it slows down (due to friction in the bearing, air resistance, etc), it loses rotational inertia because itâ€™s not spinning as fast. Therefore, itâ€™s more prone to tilting while itâ€™s slowing down (which makes sense based on what you see if you time your sleeper or something. It tilts as it slows down and vice versa)

(Your friendly neighborhood physics teacher )

**YoyoGeezer**#7

Huh?

I get that the string slows down the yoyo when it hits the walls of the gap - but what do you mean by â€ścannot feel how much center weight a yoyo has by playing with itâ€ť?

How else do you feel the weight distribution of the yoyo? I have massively rim-weighted yoyos and some that are far more evenly distributed in their weight. I can distinctly feel the difference when playing.

**dirty_birdy**#8

Yoyos cover many areas of physics. Rotational, linear, and curvilinear motion of a semi-constrained rotating body (yoyo on a string) can be described by classical mechanics. This includes everything from shape of the yoyo (mass distribution, moments of inertia, etc) to its behavior while being zipped about on a string (stability, precession, etc). One can also look at the issue of spin time and frictional forces, such as string contact with the yoyo/yoyo gap, or the entire field of bearing design and behavior (skidding, stick/slip, stiction, rolling, etc) and lubrication of moving surfaces. You could also get into the physics of the string, as there are many materials and methods for making string, soft/rough, slippery/sticky, bouncy/not-bouncy, etc. You can even go so far as to investigate things like the local aerodynamics near a spinning yoyo and figure out things like: Does a schmoove ring really do something?

Manufacturing a yoyo, be it plastic or metal, has its own set of physics as wellâ€¦

So, what part of yoyo physics are you interested in?

db

**dirty_birdy**#10

Please show me the physics equations and their application to a yoyo that gives the above conclusions.

db

**dirty_birdy**#12

First of all, please define your equation terms and units then we can talk about its application. Iâ€™d really like to see the definition of â€śsluggishnessâ€ť. Also, when trying to understand the feel and motion of the yoyo (tethered gyroscope), you need to consider every force acting on the yoyo, all realized torques, and all the couplings of torques and angular momentums. When you can draw and understand the free body diagram Iâ€™ve just described and write down all the relationships, you will plainly see that there are, indeed, off-yoyo-rotational axis forces generated while the yoyo is in linear or curvilinear motion at the end of the string. Linear inertia and rotational inertia are not directly coupled (but, they both contain the identical mass), but, once the yoyo is in motion, there is a dynamic coupling of forces and momentums

A good approach to understand this is, once you write down the complete set of governing equations for the free-body diagram of a spinning yoyo in translation at the end of a string, is to apply perturbation theory in order to see which of the cross terms have more effect on the yoyo.

db

**daniel0731ex**#14

daniel0731ex: dirty_birdy: daniel0731ex:Physics says that you cannot feel how much â€ścenter weightâ€ť a yoyo has from playing with it. It also says that sluggishness is primarily contributed by the string rather than the yoyo.

Please show me the physics equations and their application to a yoyo that gives the above conclusions.

db

The basic:

F=p/t

Rotational inertia does not affect translational inertia.

First of all, please define your equation terms and units then we can talk about its application. Iâ€™d really like to see the definition of â€śsluggishnessâ€ť. Also, when trying to understand the feel and motion of the yoyo (tethered gyroscope), you need to consider every force acting on the yoyo, all realized torques, and all the couplings of torques and angular momentums. When you can draw and understand the free body diagram Iâ€™ve just described and write down all the relationships, you will plainly see that there are, indeed, off-yoyo-rotational axis forces generated while the yoyo is in linear or curvilinear motion at the end of the string. Linear inertia and rotational inertia are not directly coupled (but, they both contain the identical mass), but, once the yoyo is in motion, there is a dynamic coupling of forces and momentums

A good approach to understand this is, once you write down the complete set of governing equations for the free-body diagram of a spinning yoyo in translation at the end of a string, is to apply perturbation theory in order to see which of the cross terms have more effect on the yoyo.

db

From my understanding, there is only two things a player can feel when the yoyo is in motion:

- The force applied to translate the yoyo
- The torque applied to alter its axis of rotation (assuming the resultant motion still has the same axis of rotation relative to the yoyo)

(itâ€™s actually still a force that is applied by the player, but for the sake of simplicity to avoid the need to take the yoyo shape into account, which is not relevant to the perception of the yoyoâ€™s mass distribution, I will discuss this in terms of torque)

For #1, it is solely determined by the overall mass of the yoyo regardless of its mass distribution. The player cannot possibly judge the â€śweight distributionâ€ť from this

For #2, it is solely determined by the overall moment of inertia of the yoyo. Yes, the player can feel the amount of axial stability achieved with regards to its mass; more center weight will mean less moment of inertia compared to its slightly more rim-weighted counterpart with the same mass, this much the player can perceive. But when people make statements such as â€śin this version they increased the center-weight on the yoyo so now it has much more axial stabilityâ€ť, that is complete blasphemy. The same axial stability could be achieved with less addition of the mass if they concentrated it to the rims.

My point here is that gimmicks such as the center-weight ring of the SFX, ODâ€™s side effects, the â€śinner ringâ€ť (or whatever it is called) from CLYW, and Mr. B!stâ€™s â€śnegative shapeâ€ť so prominently featured in the Avant Garde (which is in fact a direct replica of the Takuto.design L4, or, as YYF themselves acknowledged, a â€śhomageâ€ť) are not so much about performance than it is about durability, aesthetics, or just downright gimmicks. While it can be argued that the â€śnegative shapeâ€ť and H-shape do contribute, passively, to the performance, it is not achieved by increasing the moment of inertia of the yoyo as some people have stated.

Now, if we are to talk about the scenario of the yoyo being held in the hand, that is a whole new story.

EDIT: Parallel Axis theorem says Iâ€™m wrong. But Iâ€™ll keep the originals anyways.

**rizki_yoist**(rizkiyoist) #15

But when people make statements such as â€śin this version they increased the center-weight on the yoyo so now it has much more axial stabilityâ€ť, that is complete blasphemy. The same axial stability could be achieved with less addition of the mass if they concentrated it to the rims.

Obviously itâ€™s only modifying the total weight and has very little effect to the yoyo stability.

I thought most people shouldâ€™ve known that.

**daniel0731ex**#16

Obviously itâ€™s only modifying the total weight and has very little effect to the yoyo stability.

I thought most people shouldâ€™ve known that.

My point exactly. Yet you see fallacious statements in reviews all the time, things like â€śthe added center weight really increased the stability in horizontal combosâ€ť or â€śThe new shape design concentrates more weight towards the center which increases stability.â€ť ???

Even when referring to the yoyoâ€™s linear inertia, people say things that make no sense. Statement such as â€śthis yoyo has more center-weight which makes it play a bit slowerâ€ť is not correct; the yoyo plays â€śslowerâ€ť because it is heavier, not because of the weight distribution. The yoyo will play just as â€śslowâ€ť if all the center weight is moved to the rims, except that it will be much more stable.

At some point Iâ€™ve even seen posts like â€śthis yoyo has more rim-weight which makes it play more sluggishâ€ť

The point is, you may be able to perceive the weight distribution from how much axial stability is achieved with the overall mass of the yoyo, but you cannot judge the weight distribution itself from how the yoyo behaves in translation.

EDIT: Parallel Axis theorem says Iâ€™m wrong. But Iâ€™ll keep the originals anyways.

**MrSquirrel**#18

My science teacher asked me to bring in a stacked yoyo for our gyroscopic forces unit lol

**FiveIronBrian**#19

Oops, didnâ€™t mean to thank Shadowz, meant to thank daniel0731ex big time for explaining this!!! Total mass determines whether a yo-yo is slow or fast in translation (anything else is negligible). Mass distribution determines stability and how the force of your throw affects the initial spin.

Thanks Daniel. Thereâ€™s so much in yo-yoing thatâ€™s all in our heads.

**YoyoGeezer**#20

rizki_yoist:Obviously itâ€™s only modifying the total weight and has very little effect to the yoyo stability.

I thought most people shouldâ€™ve known that.

My point exactly. Yet you see fallacious statements in reviews all the time, things like â€śthe added center weight really increased the stability in horizontal combosâ€ť or â€śThe new shape design concentrates more weight towards the center which increases stability.â€ť ???

Even when referring to the yoyoâ€™s linear inertia, people say things that make no sense. Statement such as â€śthis yoyo has more center-weight which makes it play a bit slowerâ€ť is not correct; the yoyo plays â€śslowerâ€ť because it is heavier, not because of the weight distribution. The yoyo will play just as â€śslowâ€ť if all the center weight is moved to the rims, except that it will be much more stable.

At some point Iâ€™ve even seen posts like â€śthis yoyo has more rim-weight which makes it play more sluggishâ€ť

The point is, you may be able to perceive the weight distribution from how much axial stability is achieved with the overall mass of the yoyo, but you cannot judge the weight distribution itself from how the yoyo behaves in translation.

I do not have a degree in physics, however, my Engineering training tells me that this is not quite right.

If one cannot judge the weight distribution by itâ€™s feel in translation - how is this distribution to be realized? I think that what the person may be referring to is the amount of weight that one feels in the rims vs. the central disc of the yoyo. What does axial stability have to do with weight distribution? That is a property of the spinning gyroscope.

I wonder if what you really mean when you speak of â€śAxial stabilityâ€ť is the â€śmoment of inertiaâ€ť of the physical body. This quantity describes the tendency for the yoyo to remain in constant rotation; or rotational inertia. This moment of inertia depends on:

```
1. The axis of rotation
2. The shape of the object
3. The manner in which mass is distributed.
```

this is what many folks describe â€śfeelingâ€ť when playing the yoyo. This quantity is extremely difficult to quantify for anything but the most basic shapes due to the multi-dimensional dynamic forces at work. You simply cannot describe this quantity in simple, one-dimensional terms. This is a multivariate calculus problem.