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Author Topic: Simonelli finger top Nr. 30 - My first tungsten top  (Read 604 times)

ta0

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #15 on: October 11, 2017, 12:10:42 PM »

In most high performance tops the mass is concentrated to the outside making h even higher for I3 > I1

Interestingly, the vast majority of "high performance" tricking tops are the opposite: I3 < I1. Examples are the Giulia, STB and QSH.
A top that is too "stable" is difficult to manipulate on tricks that require the top to change the axle from vertical to horizontal: it takes too much time to make it lean.

EDIT: This is true with respect to the center of mass and, of course, even more so with respect to the tip. In addition, you need to have enough h to be able to have clearance for the string so it does not touch the rim.
« Last Edit: October 11, 2017, 12:59:38 PM by ta0 »
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Jeremy McCreary

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #16 on: October 11, 2017, 01:03:48 PM »

I stand by the statement that I3 < I1 in most real tops.

In nearly all of my tops, even the ones with external tip, the axial moment of inertia is larger than the transverse one...

No doubt, but those tops are extreme cases -- even the ones with external tips.
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Playing with the physical world through LEGO

Iacopo

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #17 on: October 11, 2017, 04:07:41 PM »

setting I1 = I3 gives h = r/2

I find this an interesting formula, which gives an immediate idea of the proportions of a top with the two moments of inertia equal.

I deduce from it that h is 0.707 times the radius of gyration in tops with I1 = I3.

In this my tungsten top h is about mm 6.5 - 7.0.
Radius of gyration mm 23.7. 
23.7 *0.707 = mm 16.75
So I should add about another 10 mm of tip under this top, for having I1 = I3
The transition shape is low but not extremely low.. 


 
« Last Edit: October 11, 2017, 04:09:54 PM by Iacopo »
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #18 on: October 11, 2017, 06:09:14 PM »

setting I1 = I3 gives h = r/2

I find this an interesting formula, which gives an immediate idea of the proportions of a top with the two moments of inertia equal.

I deduce from it that h is 0.707 times the radius of gyration in tops with I1 = I3.

True, but keep in mind that h = r/2 assumes the mass of the top is in the shape of a thin disk. Your Nr 30 top is more of a torus shape (beautiful top by the way)  Using your mass of 0.119 Kg and radius of 0.02875 m and assuming a thin disk:

I3 = 1/2(.119)(.02875)2 = 4.9x10-5 Kg m2

you give I3 = 6.7x10-5 Kg m2

which makes since because more mass is on the outside. 

By the way,  how did you get this value of I3?

Using your value of 140 rpm for the toppling down speed and using the critical speed formula I get
I1 = 3.1x10-5 Kg m2 for your Nr 30 top.
Not sure how accurate this is but it's probably in the ball park.

Edit:
For a symmetric mass distribution, its impossible to have I1 < I3/2. If h > 0 and or thickness along the symmetry axis then I1 > I3/2. So this calculation is not accurate.

Did you measure or calulate I1 for your Nr 30 top?
« Last Edit: October 12, 2017, 09:33:27 AM by Russpin »
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Iacopo

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #19 on: October 12, 2017, 02:44:31 PM »

By the way,  how did you get this value of I3?

I use a trifilar pendulum for knowing the radius of gyration, then I calculate the axial moment of inertia, knowing the weight of the top.

Using your value of 140 rpm for the toppling down speed and using the critical speed formula I get
I1 = 3.1x10-5 Kg m2 for your Nr 30 top.
Not sure how accurate this is but it's probably in the ball park.

Edit:
For a symmetric mass distribution, its impossible to have I1 < I3/2. If h > 0 and or thickness along the symmetry axis then I1 > I3/2. So this calculation is not accurate.

Maybe this top could spin for some more time and for some reason it topples down sooner ?
There is a bit of imbalance wobbling at the end of the spin, maybe this makes the top to topple sooner, but I am not sure.

H is a bit lower than I thought. I checked it again, more accurately, it is between 5.8 and 6.2 mm.

Did you measure or calulate I1 for your Nr 30 top?

I didn't. 
« Last Edit: October 12, 2017, 02:55:19 PM by Iacopo »
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #20 on: October 12, 2017, 07:00:20 PM »

I use a trifilar pendulum for knowing the radius of gyration, then I calculate the axial moment of inertia, knowing the weight of the top.

Very Cool. I would like to make one and test how accurate it is.

H is a bit lower than I thought. I checked it again, more accurately, it is between 5.8 and 6.2 mm.

I tried using h = 0.006 m and got I1 = 3.44x10-5 Kg m2. This is now over I3/2 but if I solve for I1 at the CM I get 3.0x10-5 Kg m2 which is under I3/2. So this value is still too low. This method of calculating I1 maybe just too sensitive to small errors in the inputs.

It would be interesting if you could measure I1 at the CM using your trifilar pendulum. You would have to mount the top sideways and align the CM of the top directly over the CM of the platform. This is probably easier said than done! 
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Iacopo

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #21 on: October 13, 2017, 08:59:01 AM »


I tried using h = 0.006 m and got I1 = 3.44x10-5 Kg m2. This is now over I3/2 but if I solve for I1 at the CM I get 3.0x10-5 Kg m2 which is under I3/2. So this value is still too low. This method of calculating I1 maybe just too sensitive to small errors in the inputs.

It would be interesting if you could measure I1 at the CM using your trifilar pendulum.

Done..
The transverse moment of inertia using the trifilar pendulum results 0.0000361 Kg m2.

I checked again the axial moment of inertia and realized there was an error in the calculations.  :-[
The correct data for the axial moment of inertia is 0.0000705 kg m2 and not 0.0000671.

H mm 5.8 - 6.2,   toppling down speed 140 RPM,  weight 119 grams,  radius of gyration mm 24.3


The pendulum and the calculations are described in the long comments below this video in YouTube:



As for the accuracy, I suppose the margin of error is up to about 1%.
« Last Edit: October 13, 2017, 09:08:41 AM by Iacopo »
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #22 on: October 13, 2017, 11:21:28 AM »

 Fantastic Iacopo.
Using your values for toppling down speed, mass, h and I3 into the critical speed formula gives I1 = 3.82x10-5 Kg m2 at the tip.
You measured I1 at CM to be 3.61x10-5 Kg m2. Adding the mh2 term gives I1 = 4.0x10-5 Kg m2 at the tip. All these values are over I3/2.
My calculated I1 is still a little low at CM,  I1 = 3.4x10-5 Kg m2.

Putting your measured values into the critical speed formula gives a toppling down speed of 143 RPM.
Your observed speed was 140 RPM ! Your top did better than the formula !
« Last Edit: October 13, 2017, 11:24:19 AM by Russpin »
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ta0

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #23 on: October 13, 2017, 12:01:34 PM »

Putting your measured values into the critical speed formula gives a toppling down speed of 143 RPM.
Your observed speed was 140 RPM ! Your top did better than the formula !

That's a surprisingly (to me) precise result on the calculation of the critical speed!  :o 8)

One difference between you trifilar pendulum and the torsional pendulum I have used, is that you have to use the mass of the object to calculate the moment of inertia. On the torsional pendulum you get it directly: the oscillation period is not independent of the cylinder height as it is in your video. When I have time (next week?) I'll make some measurements with a regular top.
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #24 on: October 13, 2017, 12:13:42 PM »

the oscillation period is not independent of the cylinder height as it is in your video. When I have time (next week?) I'll make some measurements with a regular top.

The moment of Inertia along the axis of a cylinder depends only on the diameter and mass. The length of the cylinder does not matter. So the radius of gyration depends only on diameter. The period of a trifilar pendulum is proportional to the radius of gyration. This is because the torque constant is proportional to mass which cancels the mass in the moment of Inertia of the test object.
« Last Edit: October 13, 2017, 12:29:16 PM by Russpin »
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ta0

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #25 on: October 13, 2017, 12:31:42 PM »

the oscillation period is not independent of the cylinder height as it is in your video. When I have time (next week?) I'll make some measurements with a regular top.

The moment of Inertia along the axis of a cylinder depends only on the diameter and mass. The length of the cylinder does not matter.
The mass of the cylinder depends of its length  ;D
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #26 on: October 13, 2017, 12:36:24 PM »

The mass of the cylinder depends of its length  ;D
Mass cancels out see my edited post above.
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ta0

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #27 on: October 13, 2017, 12:51:58 PM »

One difference between you trifilar pendulum and the torsional pendulum I have used, is that you have to use the mass of the object to calculate the moment of inertia. On the torsional pendulum you get it directly: the oscillation period is not independent of the cylinder height as it is in your video.
I don't see where what I wrote is wrong. In Iacopo's video different cylinders give the same period because it doesn't measure directly the moment of inertia. On my torsion pendulum, increasing the height of a cylinder (same density) will give slower periods as it measures directly the moment of inertia.
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Russpin

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #28 on: October 13, 2017, 01:01:30 PM »

I don't see where what I wrote is wrong. In Iacopo's video different cylinders give the same period because it doesn't measure directly the moment of inertia. On my torsion pendulum, increasing the height of a cylinder (same density) will give slower periods as it measures directly the moment of inertia.

Your torsion pendulum has a torque constant that does not depend on the weight of the test object. The torque constant on the
trifilar pendulum depends on the weight of the test object.
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ta0

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Re: Simonelli finger top Nr. 30 - My first tungsten top
« Reply #29 on: October 13, 2017, 01:05:55 PM »

Your torsion pendulum has a torque constant that does not depend on the weight of the test object. The torque constant on the
trifilar pendulum depends on the weight of the test object.
Exactly. So everything I said was correct.  ;)
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