Yoyo physics...


So I have been taking a physics class over the last 5-6 months and was wondering how some concepts from physics can be applied to yoyos. I’m not asking if (obviously laws of physics apply) but in what ways?


http://www.thomasnet.com/articles/machinery-tools-supplies/bearing-types and http://hyperphysics.phy-astr.gsu.edu/hbase/newt.html#strmas
These two articles explain pretty much how a yoyo works in terms of physics. (I did a research paper on almost this exact thing so these articles are very useful information wise)

PM Me if you have a B!ST Tondo F/T


The real question for me is … why would you wish to take such a fun thing and mix it with physics


My question is… why would you take such a fun thing and mix it with yoyos?


There are actually a series of 5 notebooks written by Don Watson that explain yo-yo physics in a much more detailed way.

I own the publishing rights to them and I’m in the process of building a website to showcase them (free) but I’m not quite done getting them all scanned and cleaned up yet.

The 5 monographs are titled

Radius of Gyration
The Academic YoYo
The Sleeping YoYo
Mechanics and Gyroscopics

There is also an unpublished gyroscope study.

I also have a copy of an article written by Wolfgang Buerger in American Scientist in 1984 on the topic.

I’ve been trying with no luck thus far to track down two books that Wolfgang also wrote (in German) about various topics like YoYos, Kites, etc. with hopes of getting them translated.

Anyway, look into topics like Moment of Inertia and Radius of Gyration to get a basic understanding of what’s going on.



Moment of inertia was exactly what I was expecting to hear about. So is this like when we are talking about the stability of yoyos, they have a greater moment of inertia due to the mass being concentrated in more of a ring/ hoop shape (the rims) than being evenly distributed across the object?

Essentially what I’m asking is does a higher moment of inertia make the yoyo more stable and spin longer? If so, why?

({RTD} alecto) #7

i haven’t quite gone into the study of the physics of yoyos as much, but i have done a lot of trial and error of how the mass of a yoyo affects it spin time. The study into the distribution of weight in a yoyo can be fascinating at times.


Moment of inertia (I) is the resistance to change in angular momentum (L), so the higher the moment of inertia, the more the yoyo will resist a change in angular momentum. So yoyos with high moments of inertia will spin longer (but they will spin slower).

The moment of inertia is calculated by multiplying the mass (m) by its the position of its centre of mass ®. Yoyos with lots of rim weight have high moments of inertia as their centre of mass is located further out and that’s why they spin longer.

I don’t know how weight distribution affects the stability of the yoyo though I have a feeling that the angular velocity (w) of the yoyo likely has something to do with it.

Here are a couple formulae if that helps you understand it:
I = mr
L = Iw


I know nothing about physics. but I did hear that a yoyo can spin as fast as a F1 engine.



So you think of a yoyo as a solid cylinder instead of hoops with a cylindrical base? My first guess was thinking you would find the moment of inertia of just the rims themselves (using 1/2mr^2) and a general moment of inertia of the body of the yoyo (using mr^2). Then look at it as a ratio of rim I to body I… Maybe not I guess? (All legitimate questions, not trying to sound rude).


Moment of inertia is important, but where that moment is distributed (away from the center line, close to the center line) is also important.

The best way to model it would probably be using computer software - I don’t think you’ll get anything accurate by hand unless you break it down into parts, assuming the profile can be represented by some sort of curve.


So when people are talking about designing yoyos and they say there is a lot of numbers involved, is this what they are talking about?

({RTD} alecto) #13

this is only a small part of what they are talking about.


Yes, the most accurate way to do it is to model it on a computer, break it down into very small individual parts and add them all up. The smaller the better. I believe that some CAD programs will do that for you.


May I ask what are some of the other things?

({RTD} alecto) #16

That’s something you need to learn from someone more experienced then me.


Any basic concepts you can think of that can point me in the right direction?


Right, modern CAD software can do this with incredible precision.

There are two moments in a yo-yo… around the axis of spin, and across it. The difference between them increases or decreases stability.

To put it simply, if you have a lot of mass at a large diameter, you get a higher moment and longer spin (albeit at a lower rpm).

If you then take that mass and move it along the width of the yo-yo, you change how ‘stable’ the yo-yo is (resistance to tilt). This is why extremely wide yo-yos lose stability and narrow ones do not.

With yo-yos it’s a matter of finding an appropriate balance between these forces to give you the ‘feel’ that you’re going for.



know you physics and life becomes for more easy.


I would love to have these bound together in hardback. I can’t find mine anywhere. God Bless Captain Yo, I haven’t seen him in years.