Aristotle's wheel paradox

[anthony]

1 hour ago, Jonathan said:

 

FALSE!!!! We've told you this several times now. You keep going back to it. No one has or is claiming that there is slippage between the hub and tire. Again: No one is claiming that there is slippage between the hub and tire. That is not where the slippage occurs. The point of the comment that you quoted from Wikipedia is that there is slippage between the hub and the curb that it contacts.

J

 

Well, not quite. *Someone* has claimed slippage between hub and tire, and it's on this Wiki Page. You need to read it properly (badly written as it is also) to see that. This can't make any sense at all - if it is merely "slippage between the hub and the curb it contacts". Nope, hub and tire.

[Brant Gaede]

If you draw a line through the Earth from true pole to true pole the rotational velocity is the same all along that line. The speed increases the father one is from the line but not the time. Distance traveled increases also. Thus rotational velocity doesn't apply to this discussion except to measure wheel to wheel distance ratio after the event.

--Brant

[anthony]

24 minutes ago, Brant Gaede said:

If you draw a line through the Earth from true pole to true pole the rotational velocity is the same all along that line. The speed increases the father one is from the line but not the time. Distance traveled increases also. Thus rotational velocity doesn't apply to this discussion except to measure distance ratio after the event.

--Brant

Brant, As I recall at the equator the surface velocity is +/-1000mph, and descending going north and south. Interesting factoid, nearly all the space launch sites are near the equator for additional centrifugal-force velocity. I disagree, the causation of rotational velocity (angular and tangential) has too many applications and consequences to count, and here specifically shouldn't be overlooked. 

 

[Max]

17 minutes ago, anthony said:

"The small wheel *must* slip to cover the same distance". The one viable answer is staring you in the face, but you prefer the "slippage" theory that has no factual base?

You just don't get it, do you? The fact that the small wheel moves more than it would by just rolling is by definition called slipping, that is a simple fact and not "some theory without factual base". And nearly everybody can also see that in reality such a small wheel indeed is slipping.

 

17 minutes ago, anthony said:

Gear A will engage the chain; gear B will engage the chain. But A and B will not at the same time.

As I've said many times already.

17 minutes ago, anthony said:

You yourself have made an allusion to the tangential velocities in a wheel, but apparently it's a theory you have not tried to apply. The theory is perceivable in action and can be logically validated . It has formulations in mathematics, no doubt.  One can show it experimentally. And yet you ignore it for an explanation that contradicts the identity of wheel motion.

Again that nonsense about the "identity of wheel motion", a totally meaningless term. You apparently forget that I applied tangential velocities to show you how slipping occurs. Perhaps you should read again my post of November 29:

That is true in the rest frame of the circle, the tangential speed of the outer circle is greater than the tangential speed of the smaller circle. But wait! We are considering the system in the rest frame of the track, where we see the wheel rolling to the right. In that frame you have to add the translation speed to the speed of the points on the circles. Due to the rotation, a point on the large circle continuously changes direction. In the lower half of the figure the horizontal component of the velocity vector of that point is directed to the left. So we have to subtract that horizontal component from the speed due to the translation to the right. In our rest frame, the point is moving slower than the center. In the 6 o'clock position the tangential velocity vector is exactly directed to the left. The speed in the rest frame (subtracting now the tangential speed from the translation speed) zero. At that one moment the point stands still. That is equivalent with the condition "rolling without slipping". *) Further rolling of the circle decreases the horizontal component of the velocity vector, so the speed in the rest frame increases again.

In the upper half of the figure the opposite happens. After passing the 9 o'clock position the speed becomes greater than the translation speed of the center.At the 12 o'clock position the velocity vector points to the right and now the tangential speed is added to the translation speed, the point has now a speed twice that of the center. Logical, because after one revolution every point on the circles must have  traveled the same distance to the right, so what they lose in the lower half, they must make up for in the upper half and vice versa.

Now look at the small circle. When the segment AB of the large circle lines up with CD of line 1, around the point of zero speed, you see that the corresponding segment EF of the small circle is swept to the right along a much larger segment GH of line 2. If the small circle would roll without slipping, like the large circle, it would in the same way line up with an segment GH that is just as small as EF. But as the tangential speed of the smaller circle is smaller than that of the large circle, the amount that is subtracted from the translation speed is smaller, and therefore it doesn't cancel the translation speed at that point (as in the case of the large circle), therefore instead of zero speed, there is a net translation to the right. That net translation we call slipping, and it is very well visible in this animation.

*) For cycloid lovers: this is the point where the cusp of the cycloid touches the line.

As you see, I give at least some useful information that you can check, instead of some vague comments about the "identity of the wheel", a "floating abstraction" indeed!

 

17 minutes ago, anthony said:

Q. Why do A and B not mesh simultaneously?** 

A. Each is turning at a different velocity.

Have another look. 

(** over and above the reason of different curvatures) 

You're again evading, I've shown that different curvatures are irrelevant. If you don't believe that, you should perhaps visit a bicycle factory.

[merjet]

1 hour ago, anthony said:

A lower rate of turn for the small wheel allows it, by necessity, to travel the same distance as the outer one, in the same time, with the same forward speed and complete exactly one revolution, too - and yet, travel past its own circumference length. 

No, the “rate of turn” or rotation of the bigger and smaller sprockets in the video are the same in degrees. The video shows rolling about 1/3rd of a revolution. Showing a ½ or full revolution would make clearer what occurs. The smaller sprocket traverses the same horizontal distance as the larger one because points on the smaller one take a more efficient path. Consider the "6:00 o'clock" starting point for each. Call them Pb for the bigger sprocket and Ps for the smaller sprocket. As Pb and Ps roll to "12:00 o'clock" it is clear that Ps’s path is shorter than Pb’s. That is captured by the right half of the motion depicted in the lower image on Wikipedia. For a full revolution the different lengths of the two different paths are twice as evident.

[Jonathan]

2 hours ago, anthony said:

Well, not quite. *Someone* has claimed slippage between hub and tire, and it's on this Wiki Page. You need to read it properly (badly written as it is also) to see that. This can't make any sense at all - if it is merely "slippage between the hub and the curb it contacts". Nope, hub and tire.

Well, then go argue with that person.

When you're having a discussion with me, try to limit yourself to addressing my positions, not some unidentified someone somewhere else's.

You asked for an example in real life of a hub slipping on a "second surface."

I supplied an example.

The idea would be to remember the context and reply to my point, not to get distracted and reply to some other person's different point (if that person and differing point even actually exist in reality).

J

[Jonathan]

The issue of gear tooth size is irrelevant. No change in their size will allow for both wheels to roll freely without slippage of either over their own toothed surfaces. Making the gears on the smaller wheel proportionally smaller, or whatever Tony images, will not alter the fact that the wheels will not move if slippage is eliminated.

J

[Jonathan]

20 hours ago, Darrell Hougen said:

Hi Merlin,

I agree that Jonathan is sometimes an obnoxious jackass...

So, you're calling me an obnoxious jackass while, at the same time, claiming that you don't like name-calling? And yet I've done nothing to you. I haven't treated you poorly. WTF???

 

20 hours ago, Darrell Hougen said:

...but the fact of the matter is that his analysis of Aristotle's paradox is correct. He has also been very patient at times, going out of his way to produce illustrative videos. We all owe him a debt of gratitude for that. And, so far as I know, he hasn't taken this dispute outside of OL...

Thank you for that. I appreciate it. It makes up for the jackass comment.

J

[Jonathan]

18 hours ago, Jon Letendre said:

Hi Darrell.

I don’t dispute any of the above. I just wanted to add something to tie it all up, something more than just your “He has also been ...”

My observation has always been that he is patient until he gets obnoxious shit. Then he returns fire. Not just sometimes he’s this way, sometimes that, no. I’ve never seen him go at someone who didn’t earn it. Others may not know the previous interactions and they may think they are seeing Jonathan rip into people unearned and from nowhere, but they are just uninformed about what came before what they are seeing.

Everyone deals with obnoxious shit differently and that’s ok. Some ignore it resolutely and politely carry on with the discussion, even though the other side is not doing so. Some worship civility and beg of others that they would see its eternal, intrinsic importance. Some refuse to continue, saying why and expressing disappointment. Jonathan returns fire. They are all reasonable, defensible responses to obnoxious shit.

Thanks much, Jon!

I think what's going on here is the WWE/NFL Referee Effect. A player takes a cheap shot, or two or three, the ref happens to not see it, but when the player who got dinged retaliates, the ref is right there on top of it. It's pretty common in O-land.

J

[Jonathan]

19 hours ago, Darrell Hougen said:

Perhaps I was too hasty since I haven't been reading all the posts on OL, but I just noticed that some people are quick to engage in name calling. I'm not an absolutist when it comes to being polite. If someone is being flagrantly rude and disparaging, I'll sometimes get down in the gutter and engage in a little tit-for-tat.

I agree with the above.

Quote

 

However, I generally dislike being impolite just because someone else doesn't seem to understand something, frustration notwithstanding.

 

 

No, it's not at all about being impolite because of someone's not understanding something. It's completely about their condescension, their evading questions, immediately rejecting substantive content without even taking the time to absorb it. And their name-calling.

Initiating bad. Retaliating good.

J

[anthony]

15 hours ago, anthony said:

 If two moons are in orbit around your planet (!) and visibly stay permanently close together, but you know that one is much more distant - which one is moving faster?

If a point on the outer rim of a wheel moves at 15m per sec when revolving, does a point anywhere inside the wheel a. move faster b. move slower c. the same speed?

 

Does anyone want to reply to these? Simple logic required, not dazzling by mathematics. 

 

[Jonathan]

14 minutes ago, anthony said:

Does anyone want to reply to these? Simple logic required, not dazzling by mathematics. 

 

Before asking questions of others, you should first reply to the questions that you haven't answered:

In your own words, what do you think the author of the "Aristotle's Wheel Paradox" thought was paradoxical? What do you think that all of the eggheads who followed, and who tried to resolve the "paradox," believed to be paradoxical? Specifically what was the problem that you think they were addressing?

J

[Brant Gaede]

2 hours ago, anthony said:

Brant, As I recall at the equator the surface velocity is +/-1000mph, and descending going north and south. Interesting factoid, nearly all the space launch sites are near the equator for additional centrifugal-force velocity. I disagree, the causation of rotational velocity (angular and tangential) has too many applications and consequences to count, and here specifically shouldn't be overlooked. 

 

The locus of the focus is the paradox. Don't go off in all directions.

--Brant

[william.scherk]

Maybe if I called Tony a moronic scumbag I could get some traction ...

18 hours ago, william.scherk said:

18 hours ago, anthony said:

Rolling straight without slip, is the "feature".

Can you explain "flange squeal" on curves?

 

 

[Jonathan]

4 hours ago, anthony said:

Well, not quite. *Someone* has claimed slippage between hub and tire, and it's on this Wiki Page. You need to read it properly (badly written as it is also) to see that. This can't make any sense at all - if it is merely "slippage between the hub and the curb it contacts". Nope, hub and tire.

Okay, so I went to check if anyone in reality at Wikipedia had presented the idea of slippage between hub and tire.

Nope.

It was, as predicted, just an imaginary person in Tony's head writing imaginary things at an imaginary Wikipedia.

J

[Jonathan]

1 hour ago, william.scherk said:

Maybe if I called Tony a moronic scumbag I could get some traction ...

In O-land, such things are indeed often required.

Standard, polite conversation is usually ignored. It doesn't work.

J

[william.scherk]

#Shit4Brains

[merjet]

7 minutes ago, william.scherk said:

[video]

You put your hands tightly over your ears? You turned down the volume on your hearing aid? 

[anthony]

On 11/25/2018 at 7:53 PM, Jonathan said:

Merlin has made this same stupid comment.

So, Tony,  your "idea" here, your "argument," is that since you don't see tracks or ledges out on the road while you drive your car, the idea of them is ridiculous?

Heh.

But, wait, maybe you're just unaware and unobservant about what's out there in reality? After all, you do have a long track record of being blissfully unaware. So let's consider it as a possibility. Hmmm, might there be, out there the in reality, just waiting for Tony to notice, the conditions that he demands exist without anyone setting them up as a result of hearing about the "paradox" (who the hell knows why he and Merkin come up with this retarded objection, but humor me for the sake of argument).

Doh! I found an example right away on the Wikipedia page! Thank God that I got to it before Merlin dishonestly erased it:

A modern approximation of such an experiment is often performed by car drivers who park too close to a curb. The car's outer tire rolls without slipping on the road surface while the inner hubcap both rolls and slips across the curb; the slipping is evidenced by a screeching noise.

Oh noes, Tony! Now what?

J

 

Before he buries the evidence, this was his post. I - "don't see tracks or ledges out on the road .."etc.

But yay! lookee here. Wiki proves there are curbs! "...the conditions that he demands exist..."

(Obviously the 'slipping" there can't be anything but between tire and 'inner hubcap". Slipping on the curb makes no sense, in the context of the wheel paradox).

[Darrell Hougen]

18 hours ago, anthony said:

I feel we are talking past each other, Darrell. I haven't that I recall, talked about leveling (maybe, once, loosely) and certainly not "leaning".

To get back on point,  I believe this is all about a second 'track' for the inner wheel? Is that right? This is best depicted by the cylinders I mention. The cylinder assembly is indeed not leaning to one side--a sectional view represents two wheels, one "larger than the other" accurate to the wheel diagram.

Briefly, I maintain that placing the bottle/combined cylinders onto two tracks (one beneath the neck, the other beneath the bottle, and compensating for their radii difference) is not going to, in essence, change anything about their combined motion. The "neck" or smaller wheel, turns slower (as we know)  in the same time as the main bottle turns slightly faster, therefore without slippage, and the two finish at the same endpoint after a rotation by each.

Hi Tony,

Okay, let's put some numbers to our theory.

Let's say we have a bottle with a neck that is 1 inch in diameter and a body that is 3 inches in diameter. Then, if the bottle rolls completely around 10 times, how far does the body travel? How far does the neck travel?

distance traveled = number of revolutions * pi * diameter = N * pi * D

So, for the body of the bottle,

distance traveled = 10 * pi * 3 =~ 94.2 inches

For the neck of the bottle,

distance traveled = 10 * pi * 1 =~ 31.4 inches

Darrell

[anthony]

2 hours ago, Jonathan said:

Before asking questions of others, you should first reply to the questions that you haven't answered:

In your own words, what do you think the author of the "Aristotle's Wheel Paradox" thought was paradoxical? What do you think that all of the eggheads who followed, and who tried to resolve the "paradox," believed to be paradoxical? Specifically what was the problem that you think they were addressing?

J

Uh, you won't reply, that is for sure. 

[Darrell Hougen]

18 hours ago, anthony said:

Jesus, try harder! Does nobody get relative velocity in a circle? If two moons are in orbit around your planet (!) and visibly stay permanently close together, but you know that one is much more distant - which one is moving faster?

Okay everyone, who votes that we try to explain orbital mechanics to Tony?

[anthony]

18 minutes ago, Darrell Hougen said:

Okay everyone, who votes that I try to explain orbital mechanics to Tony?

Darrell, a simple reply suffices. 

[Darrell Hougen]

3 minutes ago, anthony said:

Darrell, a simple reply suffices.

Hi Tony,

Sorry, I couldn't resist.

In reality, if one moon were farther away from the planet than the other, it would be moving more slowly than the one that was closer. They couldn't possibly stay in sync if they were at different distances from the planet. I just found your example amusing.

Anyway, go back and look at my other post which was more serious.

Darrell

[anthony]

Okay, obviously not what I intended, but true - I take your point. I guess you take mine.

How bout simplicity: You swing a rope around your head to which are attached a weight half-way along and a weight at the end. Which moves faster?