Print

Please login or register.
1 Hour 1 Day 1 Week 1 Month Forever
Login with username, password and session length

[ta0]

Love this curtain-ring series -- especially the last one with the pen tip! My gut tells me that the spin time isn't going to end up proportional to ring density, but I'll think about it.

My gut also told me that it should be something more complicated than linear, but that's not what I got.

If we assume the air drag is proportional to the spin w then we previously got an exponential decay of the spin:

w = w₀ exp(-k/I t)

where I is the moment of inertia, w₀ the initial spin and the drag torque = k w.
If we set w to the critical spin at which the top falls, w_c, and we solve for the time t_c to get there:

t_c= I 1/k ln(w₀/w_c)

So the time it takes to fall is indeed proportional to the moment of inertia and therefore to the density, if you keep the dimensions constant and you also manage to keep the initial spin constant.   

Edit: This seems to be a general result, not just for an exponential decay. We found before: I dw/dt = - T, where T is the torque produced by air drag and tip friction and may be an arbitrary function of the spin, T(w), but does not depend on I. It can be re-written as  - 1/T(w) dw = 1/I dt.  Integrating both sides: F(w) = 1/I t, where F(w) can be a complicated function of w, but does not depend on I or t. Then t_c = I F(w_c).

[Iacopo]

Using brass instead of plastic with the same shape/dimensions will not change the air drag but will change the tip friction, being brass denser, so the advantage as for spin time should be not proportional to the flywheel density, but a bit less.
If brass is about 7 times denser than plastic, the brass top could spin maybe 4-6 times longer than the plastic one, at parity of all other factors.

[ta0]

Good point on the dependence of tip friction on weight, what I did not consider. Tip friction torque is proportional to weight and independent of rotational speed. The question is how big it is with respect to air drag. Given that the tip and mirror are hard surfaces and even the brass ring would be relatively light, plus the critical spinning speed not very low, I expect the air drag to be dominant.

[Iacopo]

The question is how big it is with respect to air drag. Given that the tip and mirror are hard surfaces and even the brass ring would be relatively light, plus the critical spinning speed not very low, I expect the air drag to be dominant.

I too expect the air drag to be dominant, even if I guess that there could be still some influence of the tip friction, but I might be wrong, because I have no data for so light/little tops.

[ortwin]

Curtain-Ring-Top Nr.7 



This is another quick one.  I just thought of this possibility today. One of the best things about it, is the material to build it: The curtain ring, the bead and the rubber ring have all quite different functions in the spinning top, but they are topologically equivalent. - And hereby I finally had the chance to use the words "spinning top" and "topology" in the same sentence. Has any one of you ever been asked if topology is the science of spinning tops?
https://youtu.be/O9X5b0DmPt4
Since there is no need for a hole in the curtain ring for this one, I could also build it using my wedding ring without harming it.



But actually I think it was the other way around: I thought of a way how I could use my wedding ring with its high density as a flywheel for a top without drilling holes into it. Since it was easier, I still did the curtain ring model first.
Now if you take real expensive pearl as the bead here, and some fancy material instead of the rubber band, you would have a nice way to propose - if your partner is into tops at all.
https://youtu.be/kwP3nI03G8A
Although I used gold with four Platinum points as a flywheel, the spinning times are not great. Oh well, that was to be expected and not really the goal in this one.

[Jeremy McCreary]

Love this latest version! But the dog's giving me the stink-eye. Will look at videos after her walk...

And hereby I finally had the chance to use the words "spinning top" and "topology" in the same sentence. Has any one of you ever been asked if topology is the science of spinning tops?

Some guys have all the the luck!

By now, tens of thousands of all ages have seen my LEGO tops at various exhibitions. Usually get lots of questions, some technical, but never that one. Kinda glad, too. Have you ever tried to explain what topology really deals with? Besides, most it's way above my pay grade.

Lucky for us math geeks, though, topology does come up in both top design and modular construction.

[Jeremy McCreary]

Curtain-Ring-Top Nr.7 
One of the best things about it, is the material to build it: The curtain ring, the bead and the rubber ring have all quite different functions in the spinning top, but they are topologically equivalent.

Thought I understood that at first, but on 2nd thought, maybe not.

Now if you take real expensive pearl as the bead here, and some fancy material instead of the rubber band, you would have a nice way to propose - if your partner is into tops at all....

Although I used gold with four Platinum points as a flywheel, the spinning times are not great.

Strong argument for a simple wedding band! Question is, how does the recipient of your last proposal feel about these experiments?

Q: Why do you think the gold ring performed under expectations in this configuration?

[ortwin]

Curtain-Ring-Top Nr.7 
One of the best things about it, is the material to build it: The curtain ring, the bead and the rubber ring have all quite different functions in the spinning top, but they are topologically equivalent.

Thought I understood that at first, but on 2nd thought, maybe not.

https://www.britannica.com/science/topological-equivalence

Basically all three parts of the top are some things with exactly one hole in them and one type of substance around that hole. To my understanding that makes them topological equivalent. But probably subconsciously the goal was to create that sentence with "spinning top" and "topologically" in it.

Strong argument for a simple wedding band! Question is, how does the recipient of your last proposal feel about these experiments?

Q: Why do you think the gold ring performed under expectations in this configuration?

 

She was very worried and skeptical when she saw how I was playing with the wedding band. But then again I conducted experiments with it before to check for its diamagnetic properties. So she knows that my wedding band is being abused from time to time.

The gold ring did not really perform under expectation in this configuration. The rubber band is really soft and wiggly and unstable here. No comparison to the nylon line used in CRT Nr. 6 for example. Positioning the tip in the center of the ring is therefore not only a matter of luck, it also very unstable even if you by chance have it in the center at one point.

[the Earl of Whirl]

I have always enjoyed spinning my gold wedding ring, but that is just on its side.  Still, it is moving and makes the Earl of Whirl happy!!!

[ta0]

That was an ingenious way of making a top without having to cut or glue anything but just stretching and deforming. No doubt a very topological top. 

In Don Olney's 1994 book (The Tops Book, not to be confused with The Little Book of Tops) he calls his classification of tops Top-ology.

[ortwin]

Curtain-Ring-Top Nr. 8 - 4 spokes, tungsten carbide tip, wind up starter included



I bought a ball pen that had a 1 mm tungsten carbide tip. The ink is still all over the top as you can see in the pictures. It is also still on my fingers. Of course it makes no difference in this top, here a pencil would work at least as well. Anyways, it is the "wind up starter mechanism" I wanted to test. It is not great, a traditional finger start works a lot better.  With a little bit more complication, something that works much better would be possible.

https://youtu.be/T1_KO_fuqOU

[ta0]

This curtain-ring-top collection is getting quite big!  I might separate it into its own thread.

I'm trying to think if I have a top where the starting spring/elastic mechanism stays with the top and I cannot think of one. That's a very nice compact design that adds practically no mass to the top. Nice!

PS: What are you spinning it on? It looks like the front glass of a tablet, over some adjustable base, over a board game. 

[ortwin]

This curtain-ring-top collection is getting quite big!  I might separate it into its own thread.

PS: What are you spinning it on? It looks like the front glass of a tablet, over some adjustable base, over a board game. 

I think there is only one more to come, I had planned to make a separate thread after that , starting with a presentation of all of them. But I follow your suggestions, what ever you think works best.
I am actually glad you are asking about the base! 
What you see as a board game is just a place mat. 
The adjustable base is a left over of a phase of the levitron experiments.
The front glass of the tablet I chose for different reasons : The mirror bases I also use I find sometimes too concave. Here I make the surface a bit concave with the  suction cup you see on the back side. With heavy tops even that is not needed, the weight of the top makes the surface concave by itself.

Actually I want to test a sapphire base at some stage. This is the test before the test: there are sapphire screen protectors for some smart phone models available (around € 50,-). They seem to be flexible enough from what I see on pics in the net, to make them a bit concave like I tested with this tablet touch screen. I suggested the sapphire screen protectors to Iacopo somewhere in this(?) thread.

[ortwin]

I'm trying to think if I have a top where the starting spring/elastic mechanism stays with the top and I cannot think of one. That's a very nice compact design that adds practically no mass to the top. Nice!

Do we think a starting mechanism like this would be "legit" for  a long spin record? No, of course not! But how would we word the rules that exclude it? "Moving parts" can become quite a relative expression when one thinks of spokes that are somewhat flexible.

 It just might be that this picture I saw a few days ago gave me the idea for this "wind up mechanism".

or maybe this one?

[Jeremy McCreary]

This curtain-ring-top collection is getting quite big!

I think there is only one more to come....

No, no, please don't stop! I'm enjoying these. That built-in elastic starter is pretty cool.