yoyo physics

(Former National 4A Champion) #1

Alright, so i think someone was saying in another thread that a yoyos weight distribution does affect how speedy it is.

I started this thread because I would love to discuss it, but it would be off-topic on the other thread.

My view is that the weight distribution has absolutely no affect on the speed of the yoyo once it is thrown.

Stop me if you disagree with one of these points.

  1. Force = mass * acceleration

  2. A yoyo’s speed is basically another name for how easy it is to accelerate the yoyo.

  3. In order to be easy to accelerate, it must require a small amount of force to accelerate it.

  4. Assume the force exerted on the yoyo is constant.

  5. Thus, mass * acceleration = a constant.

  6. Thus the speed of the yoyo depends on the mass.

  7. Finally, a spinning yoyo has the same mass as a nonspinning yoyo.

  8. Since speed depends on mass, but a spinning yoyo doesn’t affect mass, it also doen’t affect speed.



Some yoyos don’t handle speed as well as others due to the weight distribution though.


As far as speed in a single axis goes it should not matter, but since we.work in all 3 dimensions there are alot of other forces that are acting against the “speed” of the yoyo when it is pulled in one direction or another. Also consider the gyroscopic affect that occurs on spinning objects. Weight distribution also affects how easily you can tilt the yoyo off of it’s axis.

Though I could be pointing out incorrect stuff. haven’t taken physics in years.


As you noted in #8; yoyo’s posses angular momentum. If the force of the angular momentum vector opposes and is larger than the gravity vector, then the spin can and does affect the yoyo yielding “float”. this is most easily demonstrated when throwing a Frisbee. In the case of the Frisbee, the cross product of the force vectors is upwards, which accounts for its ability to “float” in the air.

The math of this is complex, but angular momentum is a cross-product of the position vs. the linear momentum at any given time. Incidentally, this equation also relates why distribution of mass is so important. The distribution is often described as the “moment” of a body. This moment is crucial for calculating the total energy of the rotating system.



Physics is not generally a simple subject to most, but if you are going to lecture on the topic, please make sure you understand it first before writing since you don’t know which impressionable minds may be reading it.

There is no force of an angular momentum vector. Angular momentum is a vector quantity, which means it has a magnitude and a direction. Angular momentum has units of [mass] x [length^2] / [time]. Gravity is the is the mutual attraction (read “force”) between two objects, each having a given mass, and is defined by Newton’s Law of gravitation. Another way to look at force is through Newton’s Second law: F = m*a, where F is the vector quantity of Force, m is the mass of an object, and a is the acceleration vector of the mass. Force is a vector quantity because it has a magnitude and a direction and has units of [mass] x [length] / [time^2].

Angular momentums and forces are different physical quantities having different fundamental units, like apples and oranges…they cannot be compared, equated, or balanced. An angular momentum vector may point in the opposite direction of the local gravity vector, but since it is not a force, it will never counter the force of gravity. I’ll talk about the Frisbee shortly.


(Ian) #6

This astronaut talks about angular momentum regarding yoyos. 
He starts talking about physics around 3:05.

(Former National 4A Champion) #7

Actually, the reason a frisbee floats is that the rotation causes the frisbee to stay horizontal, creating the largest cross section possible, and the most air resistence possible. Even if that were true, a yoyo has two halves, which would offset each other.

The force of gravity is a linear force.
The angular momentum is angular, and not a force, so it can’t counteract gravity at all.

Once a yoyo is thrown, it can’t really have a quality called float. Any perception of float after the throw is not caused by the yoyo. Granted some yoyos have larger cross sections than others, but the cross sections are not large enough to create any significant air resistence.

Correct, but it doesn’t affect the speed itself.

I’m speaking of the common definition of a fast yoyo. What I’m trying to say is that a fast yoyo is nothing more than a light yoyo.

above two posts was made while I was typing, but here it is anyway.


Whilst I know nowhere near enough about physics to comment on what’s actually going on, I agree that weight does play a big part in play speed purely from experience.

Take as practical examples, identical models made out of different aluminium.

  1. Supernova Lite
  2. Supernova 7075

Despite being exactly the same shape and size, the lite plays considerably faster. The same is also true with the 6061 .vs. 7075 2Sickyoyos Gambit, with the lighter 6061 playing a lot faster than it’s hefty-er brother.

I used to be under the impression that weight distribution was the be-all-and-end-all of yoyo playing speed, but I soon discovered that in practical use, 'tis not the case.

(rizkiyoist) #9

I will say in a simpler way.
Weight distribution doesn’t affect speed, true.
Total weight affect speed, true.
But if a yoyo has too much rim weight, it gets sluggish in the initial throw, forcing you to accelerate before actually going fast, this gets annoying (for me at least). With less rim weight, you have to flick your hand faster to put equal force, even if it has more total weight, it “feels” faster because it’s already fast since the beginning.
That being said, weight distribution doesn’t affect speed, but in a way it helps you going fast.

Generally speaking, it’s easier for me to play fast with 67g yoyo with less rim weight than 65g full rim weight, because with less rim weight it feels like I’m doing running start instead of starting from full stop.

(Former National 4A Champion) #10

good explanation. That’s why I’ve been saying “after the throw” all this time, because weight distribution does affect the initial throw. For me, I don’t care much about the harder throw because I can just compensate by releasing it sooner.

The problem with saying that something “feels” faster is that when new yoyoers here that, they might get the same impression as gambit had. It would be better if people called yoyos “light” instead of “fast”.


What do you mean by speed?

Is it how quickly you can get the yoyo to change directions?
How much energy it takes to accelerate the yoyo traveling in the same direction?
Is it how fast it rotates (rpm)?
Is it how fast you can get it to go down the string?

Or is it something else.

I believe that weight distribution will effect angular momentum and so will have an effect on the last two properties, but not the first. While total weight of the yoyo will likely effect all of these properties.

How do you define float?

(Former National 4A Champion) #12

I defined speed in my original post

So you agree with me.

Float is a term that people use, but can’t define. I can’t stand the term, so I don’t have any definition of it.
I think a popular meaning is that float is the hang time of a yoyo, sort of like how a frisbee floats in the air.
If that is the definition, then “float” does not exist.


F=ma is only that simple to calculate when the yoyo is moving in a straight line, which is rarely the case in yoyoing. Like kadabrium said in the other thread, once the yoyo starts moving in more circular patterns, then rotational physics start to apply. The form of Newton’s law that you would want to use there is: τ = Iα

As an illustration of this: the length of your string can also affect how fast you can play. If you’ve never tried comparing long strings to short strings, you can see the basic effect easily by swinging a yoyo around in a circle on the end of the string. If you swing the yoyo from the end of the string, and then grab the string halfway up and swing it in a circle again, it accelerates differently even though the mass of the yoyo doesn’t change (the mass of the string does change, but by a negligible amount). That’s because the moment of inertia does change when you move the mass closer to or further from the center of rotation (the same reason rim-weighting affects how long a yoyo will spin).

Changing the weight distribution of a yoyo changes its moment of inertia, so it does have an effect on how the yoyo will accelerate in a circular path given a set amount of force. It’s just a matter of how much difference it actually makes, which is kind of hard to work out on paper because measuring (or looking up) moment of inertia is harder than measuring mass, and the calculations would depend on other factors such as the radius of the circular path of the yoyo. So, there is theoretically an effect, but it’s possible that it is too small for most people to notice. Or it might not be, I have no idea.

Practically speaking, I agree with those saying that how the weight distribution affects how well the yoyo handles speed is also important. If two yoyos should theoretically have the same acceleration under the same conditions, but one requires more effort to keep under control and to maintain spin when playing at higher speeds, that is going to have a practical effect on how fast someone can play with it and how fast they perceive it to be. For example, Mosquitos are really light, but I find them kind of hard to play fast with. That depends a lot on the skill of the person using the yoyos, though, so it won’t necessarily apply to everyone the same way.

(Former National 4A Champion) #14

First of all let us get this straight: the fact that the yoyo is spinning does not at all affect any part of the physics of the yoyo other than the stability.

Actually, that makes sense.  I never really got that.  I don’t know if the difference in weight distribution would actually be noticable though.

Let’s work this out.
Suppose we have yoyo of mass m and radius r on a string of length R that we are doing around the world with.

The smaller the moment of inertia around the center of the around the world, the faster the yoyo will be.

suppose all the mass of the yoyo is at the center.  The moment of inertia is
I = mR1

now suppose all the weight is at the rims.

According to the parallel axis theorem(http://en.wikipedia.org/wiki/Parallel_axis_theorem)

  1. I = I + md1

  2. I = mr1

  3. md1 = mR1

plugging 2 and 3 into 1, we get

I = mr1 + mR1

the fractional difference of the moment of inertia when moving all weight to the rims is

(I - I)/I = (mr1 + mR1 - mR1)/mR1 =
mr1/mR1 =

It’s lunch time now, so you’ll have to do your own calculatios from there.


In an angular momentum sense, a ‘play modifier’ would be the projection of angular momentum on to the plane of symmetry and the rotational axis.

Unfortunately modeling a yoyo quantum mechanically is tricky. It has D symmetry, along with spin and angular momentum. Couple in off-axis procession as some kind of Coriolis effect, and you end up with some serious Clebsch-Gordon coefficients! The only good part is that my guess is you could model it in Hund’s Case B!

Sorry I couldn’t help it… (P.S. the above is humorous but bunk, well, apart from the symmetry…)


Ok, so let’s say the yoyo has a radius of 3cm and you are doing a trick where the yoyo is moving around a path with a radius of 15cm:

r^2/R^2 = 3^2/15^2 = .04

So moving all the weight from the center to the rims would result in a 4% increase in the moment of inertia. If you put all the weight back at the center, you could get that same increase in the moment of inertia by increasing the mass by 4%. So if we’re talking about a 66g yoyo, moving the mass to from the center to the rims is like adding 66*.04 = 2.6g to the mass. Which sounds like a big difference, but that’s going from having all the mass in the center to all the mass at the edge, which is impossible. Practical differences will be considerably smaller.

If, instead of a 15cm radius for the yoyo path, you make it 30 cm:

r^2/R^2 = 3^2/30^2 = .01

which is the same effect as adding .66g to a 66g yoyo, and again with practical differences in weight distribution being much smaller. So for wide swinging movements it isn’t likely to be noticeable at all compared to weight differences. For tighter maneuvers, it might be detectable depending on how much I actually differs between yoyos, but probably not by much.

(Former National 4A Champion) #17

^ Good job. Keep in mind that these are calculations are for circular arcs. Most tricks aren’t completely circular. For tighter maneuvers, the yoyo doesn’t travel in a circle, so that would make it nearly undetectable. Eli hops, where the yoyo moves in an almost straight line, would not at all be effected by weight distribution.


technically already done but might be easier(lol u rly) to understand for some people.

A rim weighted and a center weighted yoyo could be approximated by a ring and a circle respectively of the same total area. When stretched to cylinders(think of a c3 BTH) they d have the same total weight.
For a ring (annulus) of OD 5 and ID 4, I=(5^4 - 4^4)=369(pi/4)
For a circle of radius 3, I=3^4=81(pi/4)
On a parallel axis with r=10,

Because E=(I*ω^2)/2 at the same total energy (all work done by the same force input or W=Iαθ) the circle will move sqrt(572/346)=1.29 times as fast as the ring.

(rizkiyoist) #19

We are talking about toys here…
I rather talk about it in less “OMG WHAT ARE THOSE SYMBOLS” stuff as to avoid further confusion, because explaining means making things clearer.
I personally think floaty simply means less rim weight, or narrower gap, or less diameter, or thicker string. Basically when a yoyo resist less upon throw, low kickback some says… because “hang time” only exist in Tony Hawk Pro Skater game, not in real life, unless you managed to alter gravity, thus floaty cannot (and should not be used) to refer how long a yoyo floats in the air… The way of thinking that more mass means it’s going to be pulled by gravity faster, is actually pretty humanly intuitive somehow, but in the wrong way.


Comes back after running a forum search on “physics”. Stops first at the flame-proof underwear shelf. ;D

For my own education, I’d like to attempt a list of terminology for yoyo “dynamics”:

on-axis acceleration - throw
moment of inertia - weightiness in-throw, resistance to change in RPM
in-plane acceleration (slack string) - “floaty”
in-plane acceleration (taught string) - “swing?”
out-of-plane acceleration - wall height?
gyroscopic perturbation - non-groove (cup) grinding, horizontal play
resistance to gyroscopic perturbation - “stability”

airplane-sourced terms (roll = on-axis):
yaw (axis is co-linear w/ gravity) - “string tension”
pitch - “tilt”, sloppy throw, high walls

How’d I do? Did I miss any ways in which we shove yoyos around, and how they react?

edited because I can grammar. :stuck_out_tongue: