Aristotle's wheel paradox

[Ellen Stuttle]

On January 6, 2019 at 3:44 PM, anthony said:

Did you read the article Ellen? Tangential velocity is an objectively measurable and calculable velocity. It doesn't need to be in relation to anything. 

But - every point/circle, from the outer rim, inwards, rotates slower. Less Vt.  Depending on its radius. (That's the distance from the circle center).

"Tangential velocity" is and needs to be in relation to a tangent at the point at which it's measured.

You effectively accept the idea of an imagined tangent line in accepting the idea of tangential velocity, but you reject the idea of a particular imagined tangent line - the horizontal tangent at the 6 o'clock position - in rejecting the idea of an imagined track on which the smaller circle rolls.  

This is what I was trying to get through to you, but never mind.  Your subsequent sentence mixes up rotational speed and tangential velocity.  And then you go on in a subsequent reply to Max to make the same mix-up and you call it "nitpicking" when Max explains the thorough screw up in your thinking which results.

Hopeless.

As Max says:

23 hours ago, Max said:

You'd think this is satire, but I'm afraid it is not...

I, too, am afraid that it isn't satire.  You really are muddled beyond unmuddling.

Ellen

[anthony]

19 hours ago, Ellen Stuttle said:

"Tangential velocity" is and needs to be in relation to a tangent at the point at which it's measured.

You effectively accept the idea of an imagined tangent line in accepting the idea of tangential velocity, but you reject the idea of a particular imagined tangent line - the horizontal tangent at the 6 o'clock position - in rejecting the idea of an imagined track on which the smaller circle rolls.  

This is what I was trying to get through to you, but never mind.  Your subsequent sentence mixes up rotational speed and tangential velocity.  And then you go on in a subsequent reply to Max to make the same mix-up and you call it "nitpicking" when Max explains the thorough screw up in your thinking which results.

Hopeless.

As Max says:

I, too, am afraid that it isn't satire.  You really are muddled beyond unmuddling.

Ellen

Ellen, 

If you can't "see* tangential velocity at work - in action - or read that it is a known quantity measured in meters/sec, or reason that two or more bodies revolving in synchronicity on different radii, logically rotate at different velocities -- it is you who's muddled.

Quite. A "tangent" is a theoretical line meeting the circle circumference at a point -- here, for the purpose of velocity measurement at the point. Your "tangent" you want also to be a "track". But in theory, as in the physical state, the track fails. Imagination isn't good enough validation. Fails, for the above reason which you can't accept: different speeds.

Slippage would causally occur with identical Vt speeds of the concentric wheels. Unreal as that would be. Different speeds, no slippage.

As for the correct nomenclature, this is descending into nominalism (to score points). I had repeated "tangential" velocity and Vt so often here, without making its significance heard, I tried a looser word. A good-faith debater would take the general meaning and understand the context.

 btw, I didn't "effectively accept the idea" [of tangential velocity] - I could observe its effects when first viewing the Wheel Paradox early on, but didn't know yet the term it was called. I can't believe that few still can acknowledge this evident fact of a wheel and circle (and the visual-spatial ability of some is poor) --and what it implies for resolving the paradox .

[Jonathan]

1 hour ago, anthony said:

Ellen, 

If you can't "see* tangential velocity at work - in action - or read that it is a known quantity measured in meters/sec, or reason that two or more bodies revolving in synchronicity on different radii, logically rotate at different velocities -- it is you who's muddled.

Quite. A "tangent" is a theoretical line meeting the circle circumference at a point -- here, for the purpose of velocity measurement at the point. Your "tangent" you want also to be a "track". But in theory, as in the physical state, the track fails. Imagination isn't good enough validation. Fails, for the above reason which you can't accept: different speeds.

Slippage would causally occur with identical Vt speeds of the concentric wheels. Unreal as that would be. Different speeds, no slippage.

As for the correct nomenclature, this is descending into nominalism (to score points). I had repeated "tangential" velocity and Vt so often here, without making its significance heard, I tried a looser word. A good-faith debater would take the general meaning and understand the context.

 btw, I didn't "effectively accept the idea" [of tangential velocity] - I could observe its effects when first viewing the Wheel Paradox early on, but didn't know yet the term it was called. I can't believe that few still can acknowledge this evident fact of a wheel and circle (and the visual-spatial ability of some is poor) --and what it implies for resolving the paradox .

Awww!!! Tony is just so adorable when he's pretending to be a grownup intellectual teaching people stuff!

J

[anthony]

On 1/7/2019 at 4:02 AM, Jon Letendre said:

Only the plate itself rolls without slip.

The large black circle slips, skids, it’s line.

The small black circle skids it’s line even more so than the larger one.

How else can it be, Tony? The black circles lack circumference to roll true like the plate does. Same road length, smaller then smaller again circumferences. You seriously still cannot see this simple fact?

Jon,

*Only* the circumference of the outer wheel (the plate), determines the distance covered in one revolution. OK?

Any inner circles of whatever size can do no more than conform to this distance. Which indicates they travel further than allowed by their circumferences, and seems "strange". The point of the paradox. But it's normal.

(Being smaller, naturally they "lack circumference"). 

BUT. Since their circumferences turn slower,  less Vt, they don't slip w.r.t the lines. If it were possible for them to turn the same Vt speed, then there'd be slip. 

 

[Jonathan]

1 hour ago, anthony said:

BUT. Since their circumferences turn slower,  less Vt, they don't slip w.r.t the lines. If it were possible for them to turn the same Vt speed, then there'd be slip. 

 

Jesus H.

Um, the opposite is true. A smaller wheel covering the same distance as a larger one would have to turn faster to keep up and to not slip/skid.

You have to be the stupidest person alive. Maybe even the stupidest to have ever existed.

J

[anthony]

Fine.

You've invalidated a 'track and slippage' altogether. On its own track, the inner wheel's far lesser Vt than the outer's would halt both wheels with its drag, as you admit.

And second, a wheel cannot "slip/skid" on a *line*. A "line" is theoretical. In the Paradox the inner line is simply a representation (of the firm track which the large wheel rolls upon), but elevated to perplex observers. I guess it worked.

You need to accept the reality of an inner wheel which travels further than its circumference seems to allow, which is a fact.

[Jon Letendre]

6 hours ago, anthony said:

Jon,

1) *Only* the circumference of the outer wheel (the plate), determines the distance covered in one revolution. OK?

2) Any inner circles of whatever size can do no more than conform to this distance. Which indicates they travel further than allowed by their circumferences, and seems "strange". The point of the paradox. But it's normal.

3) (Being smaller, naturally they "lack circumference"). 

4) BUT. Since their circumferences turn slower,  less Vt, they don't slip w.r.t the lines. If it were possible for them to turn the same Vt speed, then there'd be slip. 

 

1) No one imagines otherwise, Tony. I think you have asserted that and I have confirmed it at least six times.

2) Correct. And yes, it’s normal. Again, you are boldly asserting things all of us understand well.

3) lack circumference to what? —> to roll the length traversed. Therefore, they must skid. The plate possesses circumference sufficient to roll the length traversed. Smaller circles do not, so they must skid their lines.

4) You are mistaken. They slip, because they do not have the circumferential length required to roll without slip. How much circumferential length is required to roll without slip? The amount the plate has. Any less must be made up somehow — so they slip.

One more time:

The plate possesses the circumferential length required to roll without slip.

The circles have less than that.

Anither way:

To roll without any slipping a circle would have to have as much circumferential length as the plate has.

[Jon Letendre]

2 hours ago, anthony said:

Fine.

1) You've invalidated a 'track and slippage' altogether. On its own track, the inner wheel's far lesser Vt than the outer's would halt both wheels with its drag, as you admit.

2) And second, a wheel cannot "slip/skid" on a *line*. A "line" is theoretical. In the Paradox the inner line is simply a representation (of the firm track which the large wheel rolls upon), but elevated to perplex observers. I guess it worked.

3) You need to accept the reality of an inner wheel which travels further than its circumference seems to allow, which is a fact.

1) I don’t know what you are talking about.

2) Of course it can. You can’t do it, but their interaction can be analyzed. Max has explained this to you many times at several levels of detail. You do not understand.

3) We all well understand this fact, Tony. Another bold assertion as though someone here thought otherwise. No one thought otherwise.

You are deeply confused, Tony. It’s too bad you don’t perceive that fact, change away from the professor mindset and learn something, correct your thinking. You don’t seem to notice that you should be listening and then possibly learning from say, Max, not arguing with him. That amazes me.

[Jon Letendre]

6 hours ago, anthony said:

Jon,

*Only* the circumference of the outer wheel (the plate), determines the distance covered in one revolution. OK?

Any inner circles of whatever size can do no more than conform to this distance. Which indicates they travel further than allowed by their circumferences, and seems "strange". The point of the paradox. But it's normal.

(Being smaller, naturally they "lack circumference"). 

BUT. Since their circumferences turn slower,  less Vt, they don't slip w.r.t the lines. If it were possible for them to turn the same Vt speed, then there'd be slip. 

 

The plate has just started rolling, it has completed only about 1/8th rotation.

The blue circle has traversed the same length (lines) the plate has traversed.

The plate has applied circumference to road (arc) that matches road length traversed.

But the blue circle has not applied circumference length  sufficient to explain all the road traversed.

When we analyze the interaction of small wheel on its line, we find that it rotates and also skids its line.

 

[merjet]

On 1/7/2019 at 5:24 PM, Jon Letendre said:

Done, dumb jackass.

Now let’s see if you respond with more rational argument than “hogwash.”

 

On 1/7/2019 at 5:26 PM, Jon Letendre said:

god you are stupid.

You're like Jonathan – pure ad hominem, entirely lacking any rational argument.

LOL, stupid, dumb jackass. Your assertions fail the task. Try proving that the circumference of the disk equals the distance its center travels from one end to the other end. That answers the retard Jonathan's question, too.

[Brant Gaede]

32 minutes ago, merjet said:

 

You're like Jonathan – pure ad hominem, entirely lacking any rational argument.

LOL, stupid, dumb jackass. Your assertions fail the task. Try proving that the circumference of the disk equals the distance its center travels from one end to the other end. That answers the retard Jonathan's question, too.

After 73 pages everybody is locked into their positions of which there are two: rational and irrational. The latter can't answer the former but keeps pretending to. One is delusional, one is not and the others are what they are. When ideas take over the brain it's dogmatism. On a larger scale that's what happened to Objectivism starting from day one, a moralizing philosophical speech rational for its fictional world and half and half for the world of reality. That worked for the basic principles and that worked back then. Like credit and bullshit dogmatism works until it doesn't work. Then reality slaps the miscreants down. 

--Brant

[Jonathan]

4 minutes ago, Brant Gaede said:

...it's dogmatism...

Correct. It's dogmatism:

Dogmatism made this little dog taller than the north tower of the Golden Gate Bridge.

J

 

[Brant Gaede]

LOL!

[Max]

45 minutes ago, merjet said:

Try proving that the circumference of the disk equals the distance its center travels from one end to the other end.

That's rather trivial. If a disk rolls without slipping, by definition the distance between the contact points between disk and support before and after one revolution equals the circumference of the disk. The center has always the same position and distance relative to the contact point (perpendicular, distance R), so that has also traveled a distance of the circumference of the disk.

[anthony]

13 hours ago, Jon Letendre said:

1) I don’t know what you are talking about.

2) Of course it can. You can’t do it, but their interaction can be analyzed. Max has explained this to you many times at several levels of detail. You do not understand.

3) We all well understand this fact, Tony. Another bold assertion as though someone here thought otherwise. No one thought otherwise.

You are deeply confused, Tony. It’s too bad you don’t perceive that fact, change away from the professor mindset and learn something, correct your thinking. You don’t seem to notice that you should be listening and then possibly learning from say, Max, not arguing with him. That amazes me.

I have to understand all the fantastical notions of an inner track and slip which allows the small wheel to catch up with the big one, or something  - you can apply yourself to see what I'm talking about, too. Here:

There is no way that two attached, concentric wheels will roll AND skid on two tracks. Their circumferences are turning at different speeds. They will stop dead.

Either your inner track has substance, or it is "a line". You can't have it both ways. That equivocation is what all the hypothesizing has rested on.  Max, for one, was smart enough to realize that inserting a physical track (plus the additional friction, velocities, mass, torque) was going nowhere. 

And if you "well understand this fact" - i.e., an inner wheel which must travel further than its circumference, then you also know - it is what it is. You can't 'fix' it with applied 'slippage'. So, for what have you been arguing?

[anthony]

13 hours ago, Jon Letendre said:

The plate has just started rolling, it has completed only about 1/8th rotation.

The blue circle has traversed the same length (lines) the plate has traversed.

The plate has applied circumference to road (arc) that matches road length traversed.

But the blue circle has not applied circumference length  sufficient to explain all the road traversed.

When we analyze the interaction of small wheel on its line, we find that it rotates and also skids its line.

 

The best visual depiction of the different Vt's of inner circles. For the visuo-spatial experts who doubted that.

[merjet]

2 hours ago, Max said:

That's rather trivial. If a disk rolls without slipping, by definition the distance between the contact points between disk and support before and after one revolution equals the circumference of the disk. The center has always the same position and distance relative to the contact point (perpendicular, distance R), so that has also traveled a distance of the circumference of the disk.

Well, whoop-de-do! That's about as useful as 2 + 2 = 4 for what's needed. Now try proving that the circumference of the disk shown in the video equals the distance the disk travels in the video.

[Jonathan]

1 hour ago, Max said:

That's rather trivial. If a disk rolls without slipping, by definition the distance between the contact points between disk and support before and after one revolution equals the circumference of the disk. The center has always the same position and distance relative to the contact point (perpendicular, distance R), so that has also traveled a distance of the circumference of the disk.

The moron was referring not to disks rolling in general, but to the specific setup in the video that people have been posting. The moron's new idiotic position is that the disk's circumference is "20% longer than the distance along the wires."

He believes this because he doesn't understand perspective and how it affects measurement. He has measured the apparatus laterally without taking into account perspective foreshortening, and, in fact, without being aware of it and having no knowledge how to account for it.

I've addressed that idiocy here:

Quote

 

Um, here's a screen capture of the entire apparatus:

Do you see the vertical red rectangles that I've placed on the left and right sides of the image? They are both the same size. Notice that the one on the left is the same height as the wooden support next to it? See that? And on the other side, the wooden support appears to be shorter. Why is that?!!! Hmmm? Can you figure it out, genius?

Is the post on the right really shorter than the one on the left? If so, do the strings go downhill? When the wheel reaches the right side, do the lines end up lower than the circles to which they are currently tangential? No? They don't? So, what could explain the wooden support on the right appearing to be about 20% smaller than it actually is?

OMG, Merlin, look at this giant dog!!!

His shoulders come up to the deck of the Golden Gate bridge! He's way taller than the north tower of the bridge, but just shorter than the south tower.

Dang, it's a new paradox. How is it that the bridge deck is level when the north tower is so much smaller than the south tower? Is the giant dog a part of the solution? 

 

J

 

[Jonathan]

5 minutes ago, anthony said:

You can't 'fix' it with applied 'slippage'. So, for what have you been arguing?

He's been arguing with an idiot.

J

[Jonathan]

4 minutes ago, anthony said:

The best visual depiction of the different Vt's of inner circles. For the visuo-spatial experts who doubted that.

Who doubted it? The straw men who live in your moronic head?

J

[Jonathan]

4 minutes ago, merjet said:

Well, whoop-de-do! That's about as useful as 2 + 2 = 4. Now try proving that the circumference of the disk shown in the video equals the distance the disk travels in the video.

You've made the false assertion that the disk's circumference is "20% longer than the distance along the wires."

Prove it.

J

[merjet]

9 minutes ago, Jonathan said:

I've addressed that idiocy here:

Yeah, right, with another pile of your crapola.

[merjet]

6 minutes ago, Jonathan said:

You've made the false assertion that the disk's circumference is "20% longer than the distance along the wires."

Prove it.

You have falsely asserted that the disk rolls without slipping on the bottom of the groove, i.e. the disk's circumference equals the distance along the wires.  Prove it.

[Max]

15 minutes ago, anthony said:

The best visual depiction of the different Vt's of inner circles. For the visuo-spatial experts who doubted that.

Which visuo-spatial experts doubted that? Names please and links to the posts where they said that.

[Ellen Stuttle]

2 hours ago, Max said:

That's rather trivial. If a disk rolls without slipping, by definition the distance between the contact points between disk and support before and after one revolution equals the circumference of the disk. The center has always the same position and distance relative to the contact point (perpendicular, distance R), so that has also traveled a distance of the circumference of the disk.

That does the job right there of demonstrating that any inner circle must be slipping, since all positions of the entire configuration are always the same distance relative to the contact point.

Ellen