Why do some yoyos feel heavier than others?

	Have you noticed it? Sometimes you grab a yoyo that it's even smaller in size and has a lower mass than another and yet it feels heavier and plays differently. Why is that? The short answer: Density, the long answer: It gets interesting.

    

    Ok, I think the first thing I should do is to clarify that I'm not a physicist. I'm just a software engineer that happens to like yoyos and that still remembers some of what I learned at university. Also, I know my theory is subjective, maybe you feel different but hey, that's what the comments section is for! :D  With that out of the way, let's start.

    By definition, density is mass per unit of volume, its formula is D = m/V. What does that mean for us? It means that the bigger the yoyo (the greater the volume), the lighter it will feel... well, that's a bit simple but it's the general idea that's behind this post. You might say "But isn't a bigger yoyo heavier by nature" well, not necessarily. Take for example the Umbra by MK1 Yoyos, this is a big one but it doesn't have greater mass than some smaller yoyos (like the Ducc v1.0), so bigger doesn't mean heftier since its mass can't increase proportionally to the size because it would make the yoyo inefficient. Remember you throw it to make it spin, the more mass it has the greater the force you would need to make it spin a long time... so yeah, inefficient.

    Ok so we now know that size doesn't define how hefty a yoyo feels, What about the other variable? Shouldn't the DareDevil by GWAY Throws, for example, feel lighter than the Da Capo by Thesis Yoyos since the former has less mass? Well... it depends. As I mentioned earlier, how a yoyo feels is not a question of one factor or the other but a relation between the two of them.

    Let us go back to the DareDevil and use it as reference. The yoyo has a mass of 62.32 grams, a width of 44.00mm, gap of 4.5mm, and a diameter of 53.5mm (radius of 26.75mm). I list the gap because I feel it basically adds "air" to the volume so I remove that from the width. 

    Now if we simplify the model and decide the yoyo is a cylinder then its volume would be V=Pi*(W-G)*r^2 (Pi * (Width-Gap) * Radius * Radius). We'll make a pause here to explain that I simplified the model for clarity. The yoyo is not a cylinder and I will revisit how to get the real volume of it later on but bear in mind that having the real volume serves no purpose other than making theoretical values match. 

    Ok, so now we have all the data we need to get the density, lets do this: V = (3.14159*(44 - 4.5)*26.75*26.75)/1000 (dimensions are in mm and I want my results in cm^3) this operation gives 86.43cm^3 and since the mass = 64.01g we get that the conceptual density (that's how I'm gonna call the density acquired with this model from now on) is 0.702g/cm^3 or grams per cubic centimeter.

    "Woha, woha, woha, stop right there pal. The DareDevil is made of aluminum 7075 which has a density of 2.81g/cm^3 your numbers are funky." Well, yes, my conceptual density is different but that's because I assumed the yoyo is a cylinder when in reality is a sort-of-bell structure. To get the REAL volume we would need to construct (at least) two functions f(x)1 and f(x)2 that describe the shape of the outer wall and the inner cup respectively and then use calculus. We generate the solid of revolution for each function, then we integrate to get each solid's volume and finally we subtract f(x)2 from f(x)1 to get the volume of the resulting solid. At least that's what I think... you could also drop the yoyo in a previously measured amount of water and see how much it rises, assuming water has a density of 1g/cm^3 then that difference will be your volume. 

Images used with permission of Mark from MK1 Yoyos

    If you divide the mass by that volume then you will get the same 2.81g/cm^3 of aluminum 7075. If it were an exercise for a book, the real density would be the value used to check if your volume is right (which, by the way, should be 22.1779cm^3 for this specific yoyo... in theory. V = m/D).

In any case, the first method is too complex to put any effort in it, just trying to find out the functions that describe the aforementioned surfaces would be crazy enough to deter anyone from trying to determine the real volume of the yoyo... unless you are a junkie for punishment; and the second method is a no-go, so that's why I simplify the model and consider the yoyos (despite their shape) simple cylinder. It's worth mentioning that making our calculations like this gives us the opportunity to see how different one yoyo is from another. If we try to get the real volume then the whole thing has no meaning because all AL-6061 yoyos would have the same density.

    Ok so now we have the conceptual density... but What of it? Well, as I mentioned before, I believe this is the reason why yoyos feel and behave differently. Some of them feel like they have more of a punch when they return like they're able to retain more power when you bind 'em, while others feel floaty and nimble and return to your hand with grace instead of an angry hit. Not that any of them is better than the other, it's just differences that you can probably associate to the density and that can help you predict what to expect from a specific yoyo, and this is the whole reason why I wrote this post!

    I remember when I bought my DareDevil. I wasn't sure what to expect since it's light and small... but on my first throw, the yoyo felt solid and had character. Like a dwarf! The Umbra, on the other hand, is like an elf: tall and slender and won't sink in the snow (if you know what I mean) and I feel density is the reason for that. 

    Here I leave you with a small table showing the conceptual density of 12 of my yoyos. If you have some of them, check them and let me know if you agree with me in the comments.

Take care, stay safe and keep on yoyoing!

Click to enlarge, density is in g/cm^3

	1. Light tier: Edge Ultimatum, Umbra, Da Capo, Kapital 2. Medium tier: Speedaholic XX, Exia, Mimic, Grasshopper GTX 3. Hefty tier: Aurora, Daredevil, Phidias, Ducc v1.0