Consider a rolling wheel, with rubber tire. It's non-ideal,
the rubber flattens at the bottom, maybe an inch.

The tire, over the contact interval, works as planned:
it doesn't slide, relative to the road. Which means it's
at rest, relative to the road.

Therefore, the tire/wheel cannot achieve forward motion.
But it's a wheel, hence achieves continuous forward motion.
Therefore, first order logic is shown inconsistent.
Therefore, 1 = 2
QED

Therefore, arithmetic crumbles, and with it all science,
which depends on that. The laws of nature are thus
invalidated, and the universe implodes.

It was a nice ride, for 13 billion years, but the party's over -

--
Rich

On Wednesday, April 13, 2022 at 3:20:30 PM UTC-5, RichD wrote:
> Consider a rolling wheel, with rubber tire. It's non-ideal,
> the rubber flattens at the bottom, maybe an inch.
>
> The tire, over the contact interval, works as planned:
> it doesn't slide, relative to the road. Which means it's
> at rest, relative to the road.
>
> Therefore, the tire/wheel cannot achieve forward motion.
> But it's a wheel, hence achieves continuous forward motion.
> Therefore, first order logic is shown inconsistent.
> Therefore, 1 = 2
> QED
>
> Therefore, arithmetic crumbles, and with it all science,
> which depends on that. The laws of nature are thus
> invalidated, and the universe implodes.
>
> It was a nice ride, for 13 billion years, but the party's over -

NOBODY could really be so stupid as you pretend to be
with this post. You're just kidding and want to waste
others' time.

That's not amusing.

On Wednesday, April 13, 2022 at 10:10:59 PM UTC-4, prokaryotic.c...@gmail.com wrote:

> NOBODY could really be so stupid as you pretend to be

I reported him as spam.
You should too!

RichD <r_delaney2001@yahoo.com> wrote:
> Consider a rolling wheel, with rubber tire. It's non-ideal,
> the rubber flattens at the bottom, maybe an inch.
>
> The tire, over the contact interval, works as planned:
> it doesn't slide, relative to the road. Which means it's
> at rest, relative to the road.

The patch of tire is at rest, relative to the road. But obviously, because
the tire is rotating, the patch of tire is not at rest relative to the axle
of the wheel. Obviously also, because the axle of the wheel is moving
relative to the patch of tire, then the axle is also moving relative to the
road.

>
> Therefore, the tire/wheel cannot achieve forward motion.

Don’t you feel silly now?

Is this really the kind of thinking you put into physics?

> But it's a wheel, hence achieves continuous forward motion.
> Therefore, first order logic is shown inconsistent.
> Therefore, 1 = 2
> QED
>
> Therefore, arithmetic crumbles, and with it all science,
> which depends on that. The laws of nature are thus
> invalidated, and the universe implodes.
>
> It was a nice ride, for 13 billion years, but the party's over -
>
> --
> Rich
>

--
Odd Bodkin -- maker of fine toys, tools, tables

On April 13, prokaryotic.c...@gmail.com wrote:
>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>> the rubber flattens at the bottom, maybe an inch.
>> The tire, over the contact interval, works as planned:
>> it doesn't slide, relative to the road. Which means it's
>> at rest, relative to the road.
>> Therefore, the tire/wheel cannot achieve forward motion.
>> But it's a wheel, hence achieves continuous forward motion.
>> Therefore, first order logic is shown inconsistent.
> Therefore, 1 = 2
>> QED
>> Therefore, arithmetic crumbles, and with it all science,
>> which depends on that. The laws of nature are thus
>> invalidated, and the universe implodes.
>
> NOBODY could really be so stupid as you pretend to be
> with this post. You're just kidding and want to waste
> others' time.

Dammit, amigo, you caught me, you razor sharp sonuvagun!
The universe isn't really going to implode, and first order logic
hasn't (yet) been invalidated. I'm going to have to get out of bed
earlier, to slip anything past you -

Humor, satire, sarcasm, is a test of IQ. You didn't know that, did you?

Now to the substance - I present a PARADOX. A paradox serves as
a challenge to the student. Presumably, in solving it, he learns
something. Incredible, that I need to explain these things.

Let's review, I'll type slowly. Given two surfaces in relative motion,
opposite directions. They're in contact, therefore sliding, hence
friction, normally.

But the flattened rubber doesn't slide, it's a frictionless wheel.
NO SLIDING, NO MOTION RELATIVE TO THE ROAD.
How does the vehicle make forward progress?

This question exploded your brain... you can't resolve it, but but but...
OBVIOUSLY, the vehicle progresses! Then you lash out, as a
reflex. We need a head shrinker, for explanation -

I suggest you refrain from responding to my memos, as you
tend to misread them, and end up making a fool of yourself.
It's painful to watch.

> That's not amusing.

De gustibus non est disputandum -

--
Rich

On 4/14/2022 5:47 PM, RichD wrote:
> On April 13, prokaryotic.c...@gmail.com wrote:
>>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>>> the rubber flattens at the bottom, maybe an inch.
>>> The tire, over the contact interval, works as planned:
>>> it doesn't slide, relative to the road. Which means it's
>>> at rest, relative to the road.
>>> Therefore, the tire/wheel cannot achieve forward motion.
>>> But it's a wheel, hence achieves continuous forward motion.
>>> Therefore, first order logic is shown inconsistent.
> > Therefore, 1 = 2
>>> QED
>>> Therefore, arithmetic crumbles, and with it all science,
>>> which depends on that. The laws of nature are thus
>>> invalidated, and the universe implodes.
>>
>> NOBODY could really be so stupid as you pretend to be
>> with this post. You're just kidding and want to waste
>> others' time.
>
> Dammit, amigo, you caught me, you razor sharp sonuvagun!
> The universe isn't really going to implode, and first order logic
> hasn't (yet) been invalidated. I'm going to have to get out of bed
> earlier, to slip anything past you -
>
> Humor, satire, sarcasm, is a test of IQ. You didn't know that, did you?
>
> Now to the substance - I present a PARADOX. A paradox serves as
> a challenge to the student. Presumably, in solving it, he learns
> something. Incredible, that I need to explain these things.
>
> Let's review, I'll type slowly. Given two surfaces in relative motion,
> opposite directions. They're in contact, therefore sliding, hence
> friction, normally.
>
> But the flattened rubber doesn't slide, it's a frictionless wheel.
> NO SLIDING, NO MOTION RELATIVE TO THE ROAD.
> How does the vehicle make forward progress?

You would have a case and a cause if that particular relationship
between the tire and the road were of finite duration.

Ahhh, the marvels of infinite and zero, ain't they grand?

Can horses fly? They get airborne, no?

<https://www.google.com/imgres?imgurl=https%3A%2F%2Fpbs.twimg.com%2Fmedia%2FFGKnZ_5VgAQDDq8%3Fformat%3Djpg%26name%3D4096x4096&imgrefurl=https%3A%2F%2Fmobile.twitter.com%2FTonyD2155%2Fstatus%2F1468920501447770113&tbnid=miO_A2CpzreKPM&vet=12ahUKEwjX8t_l1ZT3AhVjcs0KHSKQAUoQMygUegUIARC-Ag..i&docid=HqCRl3000-og6M&w=4096&h=2731&itg=1&q=airborne%20horse&hl=en&ved=2ahUKEwjX8t_l1ZT3AhVjcs0KHSKQAUoQMygUegUIARC-Ag>

> This question exploded your brain... you can't resolve it, but but but...
> OBVIOUSLY, the vehicle progresses! Then you lash out, as a
> reflex. We need a head shrinker, for explanation -
>
> I suggest you refrain from responding to my memos, as you
> tend to misread them, and end up making a fool of yourself.
> It's painful to watch.
>
>> That's not amusing.
>
> De gustibus non est disputandum -
>
> --
> Rich

RichD <r_delaney2001@yahoo.com> wrote:
> On April 13, prokaryotic.c...@gmail.com wrote:
>>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>>> the rubber flattens at the bottom, maybe an inch.
>>> The tire, over the contact interval, works as planned:
>>> it doesn't slide, relative to the road. Which means it's
>>> at rest, relative to the road.
>>> Therefore, the tire/wheel cannot achieve forward motion.
>>> But it's a wheel, hence achieves continuous forward motion.
>>> Therefore, first order logic is shown inconsistent.
> > Therefore, 1 = 2
>>> QED
>>> Therefore, arithmetic crumbles, and with it all science,
>>> which depends on that. The laws of nature are thus
>>> invalidated, and the universe implodes.
>>
>> NOBODY could really be so stupid as you pretend to be
>> with this post. You're just kidding and want to waste
>> others' time.
>
> Dammit, amigo, you caught me, you razor sharp sonuvagun!
> The universe isn't really going to implode, and first order logic
> hasn't (yet) been invalidated. I'm going to have to get out of bed
> earlier, to slip anything past you -
>
> Humor, satire, sarcasm, is a test of IQ. You didn't know that, did you?
>
> Now to the substance - I present a PARADOX. A paradox serves as
> a challenge to the student. Presumably, in solving it, he learns
> something. Incredible, that I need to explain these things.
>
> Let's review, I'll type slowly. Given two surfaces in relative motion,
> opposite directions. They're in contact, therefore sliding, hence
> friction, normally.
>
> But the flattened rubber doesn't slide, it's a frictionless wheel.
> NO SLIDING, NO MOTION RELATIVE TO THE ROAD.
> How does the vehicle make forward progress?

So presumably this is a joke too.
Can a bike roll on ice?

Can you try harder?

>
> This question exploded your brain... you can't resolve it, but but but...
> OBVIOUSLY, the vehicle progresses! Then you lash out, as a
> reflex. We need a head shrinker, for explanation -
>
> I suggest you refrain from responding to my memos, as you
> tend to misread them, and end up making a fool of yourself.
> It's painful to watch.
>
>> That's not amusing.
>
> De gustibus non est disputandum -
>
> --
> Rich
>

--
Odd Bodkin -- maker of fine toys, tools, tables

On April 14, bodk...@gmail.com wrote:
>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>> the rubber flattens at the bottom, maybe an inch.
>> The tire, over the contact interval, works as planned:
>> it doesn't slide, relative to the road. Which means it's
>> at rest, relative to the road.
>
> The patch of tire is at rest, relative to the road. But obviously, because
> the tire is rotating, the patch of tire is not at rest relative to the axle
> of the wheel.

ummm... the axle is FIXED to the wheel's rotation axis.  They
rotate TOGETHER, same angular velocity.  Thus, considering
the axle as the reference co-ordinate system, each point of the
tire maintains a fixed position, relative to the axle.  

Like a rotating platform and centrifugal force, you know? In the
rotating co-ordinate system, everything is relatively motionless.

So, in what manner, exactly, is the patch of tire not at rest
relative to the wheel axle?

> Obviously also, because the axle of the wheel is moving
> relative to the patch of tire, then the axle is also moving relative to the
> road.

"Obviously"... ummm... the axle is moving relative to the patch of tire,
sez you... and you have already conceded, the tire patch is at rest,
relative to the road.

Thus, in your world, the tire doesn't make forward progress, relative
to the road. However, the axle moves, relative to the tire and road.

OK, so the car is at First and Elm St. The wheel stays in place there.
The axle continues, arriving at First and Maple... while the wheel
stays behind.

Back to the drawing board, Bod! Though you get credit for trying -

And now, here it comes... 3...2...1...

>> Therefore, the tire/wheel cannot achieve forward motion.
>
> Don’t you feel silly now?
> Is this really the kind of thinking you put into physics?

Right on cue!

--
Rich

On 4/14/22 5:47 PM, RichD wrote:
>How does the vehicle make forward progress?

You said it yourself: the rubber of the tire DEFORMS.

Tom Roberts

On Thursday, April 14, 2022 at 5:47:27 PM UTC-5, RichD wrote:
> On April 13, prokaryotic.c...@gmail.com wrote:
> >> Consider a rolling wheel, with rubber tire. It's non-ideal,
> >> the rubber flattens at the bottom, maybe an inch.
> >> The tire, over the contact interval, works as planned:
> >> it doesn't slide, relative to the road. Which means it's
> >> at rest, relative to the road.
> >> Therefore, the tire/wheel cannot achieve forward motion.
> >> But it's a wheel, hence achieves continuous forward motion.
> >> Therefore, first order logic is shown inconsistent.
> > Therefore, 1 = 2
> >> QED
> >> Therefore, arithmetic crumbles, and with it all science,
> >> which depends on that. The laws of nature are thus
> >> invalidated, and the universe implodes.
> >
> > NOBODY could really be so stupid as you pretend to be
> > with this post. You're just kidding and want to waste
> > others' time.
> Dammit, amigo, you caught me, you razor sharp sonuvagun!
> The universe isn't really going to implode, and first order logic
> hasn't (yet) been invalidated. I'm going to have to get out of bed
> earlier, to slip anything past you -
>
> Humor, satire, sarcasm, is a test of IQ. You didn't know that, did you?
>
> Now to the substance - I present a PARADOX. A paradox serves as
> a challenge to the student. Presumably, in solving it, he learns
> something. Incredible, that I need to explain these things.
>
> Let's review, I'll type slowly. Given two surfaces in relative motion,
> opposite directions. They're in contact, therefore sliding, hence
> friction, normally.
>
> But the flattened rubber doesn't slide, it's a frictionless wheel.
> NO SLIDING, NO MOTION RELATIVE TO THE ROAD.
> How does the vehicle make forward progress?
>
> This question exploded your brain... you can't resolve it, but but but...
> OBVIOUSLY, the vehicle progresses! Then you lash out, as a
> reflex.

Are you claiming that this is some sort of paradox?
The tire is not solid like a metal.
If the tire were a three-cornered solid Δ equilateral triangle
made out of steel, then you *might* have a problem, but
not with a rubber tire.

Nothing says that the position of the axle is fixed
with respect to where the tire contacts the road.

> We need a head shrinker, for explanation -
>
> I suggest you refrain from responding to my memos, as you
> tend to misread them, and end up making a fool of yourself.
> It's painful to watch.
>
> > That's not amusing.
>
> De gustibus non est disputandum -

The only fool is you, trying to make us believe that you
are so stupid as to think that you have described some
sort of paradox.

You are NOT that stupid. NOBODY is.

Tom Roberts <tjroberts137@sbcglobal.net> wrote:

> On 4/14/22 5:47 PM, RichD wrote:
> >How does the vehicle make forward progress?
>
> You said it yourself: the rubber of the tire DEFORMS.

Yes, explaining how it works for a real tire
is a nice undergraduate excercise.
Bonus points for: compute the size of the contact area,

Jan

RichD <r_delaney2001@yahoo.com> wrote:
> On April 14, bodk...@gmail.com wrote:
>>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>>> the rubber flattens at the bottom, maybe an inch.
>>> The tire, over the contact interval, works as planned:
>>> it doesn't slide, relative to the road. Which means it's
>>> at rest, relative to the road.
>>
>> The patch of tire is at rest, relative to the road. But obviously, because
>> the tire is rotating, the patch of tire is not at rest relative to the axle
>> of the wheel.
>
> ummm... the axle is FIXED to the wheel's rotation axis.  They
> rotate TOGETHER, same angular velocity.  Thus, considering
> the axle as the reference co-ordinate system, each point of the
> tire maintains a fixed position, relative to the axle.  
>
> Like a rotating platform and centrifugal force, you know? In the
> rotating co-ordinate system, everything is relatively motionless.
>
> So, in what manner, exactly, is the patch of tire not at rest
> relative to the wheel axle?

You can’t possibly be this stupid…

>
>> Obviously also, because the axle of the wheel is moving
>> relative to the patch of tire, then the axle is also moving relative to the
>> road.
>
> "Obviously"... ummm... the axle is moving relative to the patch of tire,
> sez you... and you have already conceded, the tire patch is at rest,
> relative to the road.
>
> Thus, in your world, the tire doesn't make forward progress, relative
> to the road. However, the axle moves, relative to the tire and road.
>
> OK, so the car is at First and Elm St. The wheel stays in place there.
> The axle continues, arriving at First and Maple... while the wheel
> stays behind.
>
> Back to the drawing board, Bod! Though you get credit for trying -
>
> And now, here it comes... 3...2...1...
>
>>> Therefore, the tire/wheel cannot achieve forward motion.
>>
>> Don’t you feel silly now?
>> Is this really the kind of thinking you put into physics?
>
> Right on cue!
>
> --
> Rich
>

--
Odd Bodkin -- maker of fine toys, tools, tables

On April 14, tjrob137 wrote:
>> How does the vehicle make forward progress?
>
> You said it yourself: the rubber of the tire DEFORMS.

That doesn't explain the paradox, that's the basis of the paradox!

Le'ts follow your thought further - the tire deforms,
hence the wheel is non-ideal. So, shrink the deformation,
the interval length in road contact, down to zero, a point
contact, the ideal case.

Then, with no deformation, the wheel can't progress? Is that your position?

--
Rich

On April 14, prokaryotic.c...@gmail.com wrote:
>>>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>>>> the rubber flattens at the bottom, maybe an inch.
>> Let's review, I'll type slowly. Given two surfaces in relative motion,
>> opposite directions. They're in contact, therefore sliding, hence
>> friction, normally.
>> But the flattened rubber doesn't slide, it's a frictionless wheel.
>> NO SLIDING, NO MOTION RELATIVE TO THE ROAD.
>> How does the vehicle make forward progress?
>
> Nothing says that the position of the axle is fixed
> with respect to where the tire contacts the road.
> The only fool is you, trying to make us believe that you
> are so stupid as to think that you have described some
> sort of paradox.

yawn
No relative motion between the flattened tire interval and road.

Your brain reminds me of the sun - continuously exploding,
never runs out of fuel -

--
Rich

RichD <r_delaney2001@yahoo.com> wrote:
> On April 14, tjrob137 wrote:
>>> How does the vehicle make forward progress?
>>
>> You said it yourself: the rubber of the tire DEFORMS.
>
> That doesn't explain the paradox, that's the basis of the paradox!
>
> Le'ts follow your thought further - the tire deforms,
> hence the wheel is non-ideal. So, shrink the deformation,
> the interval length in road contact, down to zero, a point
> contact, the ideal case.
>
> Then, with no deformation, the wheel can't progress? Is that your position?
>
> --
> Rich
>

The wheel cannot *accelerate* without the application of friction force
between the tire patch and the road.

The wheel can “progress” at constant speed with or without friction.
Anybody who has rolled a smooth, hard ball (such as made of glass or steel)
on smooth ice knows that the ball will “progress” whether there is relative
motion between the bottom surface of the ball and the ice or not. In the
case of zero friction, the rotation of the ball is irrelevant because the
slipping between the surfaces is irrelevant.

If a wheel has tangential speed v, this *means* that relative to the center
of the wheel the top of the wheel has speed v in one direction, and the
bottom of the wheel has speed v in the opposite direction. Now map that
with a Galilean transform to a frame where the bottom of the wheel has
instantaneous speed zero, then the center of the wheel has speed v in the
forward direction, and the top of the wheel has speed 2v in the forward
direction.

To first order, the deformation of the tire doesn’t affect the friction at
all. You can perform this experiment yourself. Given a box with relative
dimensions 1x3x9, if you rest the box on the 1x3 surface, you will
encounter the same static friction as you would if you rested it on the 3x9
surface, even though the surface areas are different by a factor of 9. This
changes somewhat with tread, but that has more to do with shear
deformation.

--
Odd Bodkin -- maker of fine toys, tools, tables

On April 13, RichD wrote:
> Consider a rolling wheel, with rubber tire. It's non-ideal,
> the rubber flattens at the bottom, maybe an inch.
> The tire, over the contact interval, works as planned:
> it doesn't slide, relative to the road. Which means it's
> at rest, relative to the road.
> Therefore, the tire/wheel cannot achieve forward motion.

All right, I'll offer my own solution.

Switch viewpoints to the wheel frame. You are sitting on one
of the spokes, looking straight outward. This takes some
visualization. [it really begs for an animation]

The wheel rotates cw, relative to the road; in your frame, you
see the flattened rubber interface rotating ccw. Again, no
relative motion between tire interval and road, no sliding, no
friction. How to explain forward progress?

As the rubber continually deforms, the interval length remains
constant. But there's a leading vertex, where it meets the road,
and a trailing vertex, which lifts. Along the length, the road
presses INTO the rubber, but no sliding friction. At the vertices,
the pressure is likewise normal - up or down - so again, no sliding.

Thus the road does move relative to the tire surface. (duh)
The key point is there's never any TANGENTIAL motion at the
interface, the pavement continually lifts and falls.

The subtle, tricky part is the assertion of no relative motion
between rubber interval and road. True: no tangential parallel
motion, but also false: a complicated rotational motion, pressing
and lifting, as the road orbits around the wheel.

That's my story, and I'm sticking to it, unless someone can offer
something better -

--
Rich

On Friday, April 15, 2022 at 3:31:25 PM UTC-5, RichD wrote:

> That's my story, and I'm sticking to it, unless someone can offer
> something better -

I was wrong. You really ***ARE*** that stupid. And here I was
asserting that NOBODY could possibly be so stupid.

RichD <r_delaney2001@yahoo.com> wrote:
> On April 13, RichD wrote:
>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>> the rubber flattens at the bottom, maybe an inch.
>> The tire, over the contact interval, works as planned:
>> it doesn't slide, relative to the road. Which means it's
>> at rest, relative to the road.
>> Therefore, the tire/wheel cannot achieve forward motion.
>
> All right, I'll offer my own solution.
>
> Switch viewpoints to the wheel frame. You are sitting on one
> of the spokes, looking straight outward. This takes some
> visualization. [it really begs for an animation]
>
> The wheel rotates cw, relative to the road; in your frame, you
> see the flattened rubber interface rotating ccw. Again, no
> relative motion between tire interval and road, no sliding, no
> friction. How to explain forward progress?
>
> As the rubber continually deforms, the interval length remains
> constant. But there's a leading vertex, where it meets the road,
> and a trailing vertex, which lifts. Along the length, the road
> presses INTO the rubber, but no sliding friction. At the vertices,
> the pressure is likewise normal - up or down - so again, no sliding.
>
> Thus the road does move relative to the tire surface. (duh)
> The key point is there's never any TANGENTIAL motion at the
> interface, the pavement continually lifts and falls.
>
> The subtle, tricky part is the assertion of no relative motion
> between rubber interval and road. True: no tangential parallel
> motion, but also false: a complicated rotational motion, pressing
> and lifting, as the road orbits around the wheel.
>
> That's my story, and I'm sticking to it, unless someone can offer
> something better -
>
> --
> Rich
>

I’m a little surprised this was not all covered for you in introductory
physics.
It is well known and afaik always taught that rolling is an example of
static friction, not kinetic friction. The coefficient of static friction
is generally higher than the coefficient for kinetic friction, which is why
you’ll have better control if you’re rolling than if you’re skidding. This
is why, for example, you should turn into a skid (among other reasons) and
why you should slow hard but not lock wheels if you can at all help it in
an emergency stop.

--
Odd Bodkin -- maker of fine toys, tools, tables

Prokaryotic Capase Homolog <prokaryotic.caspase.homolog@gmail.com> wrote:
> On Friday, April 15, 2022 at 3:31:25 PM UTC-5, RichD wrote:
>
>> That's my story, and I'm sticking to it, unless someone can offer
>> something better -
>
> I was wrong. You really ***ARE*** that stupid. And here I was
> asserting that NOBODY could possibly be so stupid.
>
>

I too am deeply disappointed.

It was one thing when RichD was a bag of tossed word salad and random
reference generator.

It’s another thing when he turns to high school physics and botches it.

--
Odd Bodkin -- maker of fine toys, tools, tables

On 4/15/2022 4:10 PM, Odd Bodkin wrote:
> RichD <r_delaney2001@yahoo.com> wrote:
>> On April 14, tjrob137 wrote:
>>>> How does the vehicle make forward progress?
>>>
>>> You said it yourself: the rubber of the tire DEFORMS.
>>
>> That doesn't explain the paradox, that's the basis of the paradox!
>>
>> Le'ts follow your thought further - the tire deforms,
>> hence the wheel is non-ideal. So, shrink the deformation,
>> the interval length in road contact, down to zero, a point
>> contact, the ideal case.
>>
>> Then, with no deformation, the wheel can't progress? Is that your position?
>>
>> --
>> Rich
>>
>
> The wheel cannot *accelerate* without the application of friction force
> between the tire patch and the road.
>
> The wheel can “progress” at constant speed with or without friction.
> Anybody who has rolled a smooth, hard ball (such as made of glass or steel)
> on smooth ice knows that the ball will “progress” whether there is relative
> motion between the bottom surface of the ball and the ice or not. In the
> case of zero friction, the rotation of the ball is irrelevant because the
> slipping between the surfaces is irrelevant.
>
> If a wheel has tangential speed v, this *means* that relative to the center
> of the wheel the top of the wheel has speed v in one direction, and the
> bottom of the wheel has speed v in the opposite direction. Now map that
> with a Galilean transform to a frame where the bottom of the wheel has
> instantaneous speed zero, then the center of the wheel has speed v in the
> forward direction, and the top of the wheel has speed 2v in the forward
> direction.
>
> To first order, the deformation of the tire doesn’t affect the friction at
> all. You can perform this experiment yourself. Given a box with relative
> dimensions 1x3x9, if you rest the box on the 1x3 surface, you will
> encounter the same static friction as you would if you rested it on the 3x9
> surface, even though the surface areas are different by a factor of 9. This
> changes somewhat with tread, but that has more to do with shear
> deformation.
>
Also remember, this: Although it may seem contradictory, the patch of
the tire has static friction with the road. This is because the patch
is stationary relative to the road.

If the tire has dynamic friction, it means one of three things:
1) You've locked the brakes up and the wheel isn't spinning;
2) You're burning rubber;
3) You're sliding on ice and are about to crash...

Dynamic friction is less than static friction, which is why you don't
want to lock the brakes in a panic stop (and most cars have antilock
brakes anyway)

RichD wrote:

> Consider a rolling wheel, with rubber tire. It's non-ideal,
> the rubber flattens at the bottom, maybe an inch.
>
> The tire, over the contact interval, works as planned:
> it doesn't slide, relative to the road. Which means it's
> at rest, relative to the road.

No, it is not. Instead, it would remain at rest relative to the road if it
slid completely and would not “flatten at the bottom”.

The problem with your argument is a semantic fallacy (perhaps out of
ignorance): You are confusing “at rest relative to the road” with “in
contact with the road”. The former basically means that the wheels position
relative to the road would not change.

To keep it simple, we would make use of the rotational symmetry of the
situation and define the position of the wheel relative to the road by the
horizontal position of its center of rotation. Certainly you can see that
then the position of the wheel, if it is rolling on the road, changes
relative to the road insofar as that it changes relative to a fixed point on
the road.

And even if you do not agree with that choice, certainly you can see that a
fixed point on the rubber of the wheel is in a continuous, oscillating
motion relative to (any point on) the road. (That is what “rolling”
*means* in contrast to “sliding”.)
> Therefore, the tire/wheel cannot achieve forward motion.

Ex falso quodlibet.

> But it's a wheel, hence achieves continuous forward motion.

Because there is friction between it and the road and (ideally) it does NOT
slide at all.

Also, note that forward motion on wheels does not require rolling. Once the
car is in motion relative to the road, it can also slide on the road – a
fact that becomes most important when the road is wet, so that the driver
and tire manufacturers have to find ways to avoid/counteract aquaplaning.

<https://en.wikipedia.org/wiki/Aquaplaning>

Finally, the relation of your posting to the theories of relativity is
tenuous at best.

PointedEars
--
«Nec fasces, nec opes, sola artis sceptra perennant.»
(“Neither high office nor power, only the scepters of science survive.”)

—Tycho Brahe, astronomer (1546-1601): inscription at Hven

RichD wrote:

> Consider a rolling wheel, with rubber tire. It's non-ideal,
> the rubber flattens at the bottom, maybe an inch.
>
> The tire, over the contact interval, works as planned:
> it doesn't slide, relative to the road. Which means it's
> at rest, relative to the road.

No, it is not. Instead, it would remain at rest relative to the road if it
slid completely and would not “flatten at the bottom”.

The problem with your argument is a semantic fallacy (perhaps out of
ignorance): You are confusing “at rest relative to the road” with “in
contact with the road”. The former basically means that the wheel‘s
position relative to the road would not change.

To keep it simple, we would make use of the rotational symmetry of the
situation and define the position of the wheel relative to the road by the
horizontal position of its center of rotation. Certainly you can see that
then the position of the wheel, if it is rolling on the road, changes
relative to the road insofar as that it changes relative to a fixed point on
the road.

And even if you do not agree with that choice, certainly you can see that a
fixed point on the rubber of the wheel is in a continuous, oscillating
motion relative to (any point on) the road. (That is what “rolling”
*means* in contrast to “sliding”.)
> Therefore, the tire/wheel cannot achieve forward motion.

Ex falso quodlibet.

> But it's a wheel, hence achieves continuous forward motion.

Because there is friction between it and the road and (ideally) it does NOT
slide at all.

Also, note that forward motion on wheels does not require rolling. Once the
car is in motion relative to the road, it can also slide on the road – a
fact that becomes most important when the road is wet, so that the driver
and tire manufacturers have to find ways to avoid/counteract aquaplaning.

<https://en.wikipedia.org/wiki/Aquaplaning>

Finally, the relation of your posting to the theories of relativity is
tenuous at best.

PointedEars
--
«Nec fasces, nec opes, sola artis sceptra perennant.»
(“Neither high office nor power, only the scepters of science survive.”)

—Tycho Brahe, astronomer (1546-1601): inscription at Hven

On April 15, Thomas 'PointedEars' Lahn wrote:
>> Consider a rolling wheel, with rubber tire. It's non-ideal,
>> the rubber flattens at the bottom, maybe an inch.
>> The tire, over the contact interval, works as planned:
>> it doesn't slide, relative to the road. Which means it's
> > at rest, relative to the road.
>
> No, it is not. Instead, it would remain at rest relative to the road if it
> slid completely and would not “flatten at the bottom”.

Say what???
If the tire slides along the road, it's MOVING relative to the road!
(and then friction defeats the whole purpose)

The rubber flattens, maybe 3 inches. Call this the track.

The points along the track DON'T slide, each point remains
in contact with a corresponding point on the pavement,
that's what "no relative motion" means.

Eventually, a point on the track moves to the rear, and lifts.
After that, it moves relative to the road (obviously).

> The problem with your argument is a semantic fallacy (perhaps out of
> ignorance): You are confusing “at rest relative to the road” with “in
> contact with the road”.

I never commit semantic fallacies.

I do not confuse these ideas. The track is in continuous
contact with the road. And each point of the rubber along
the track, contacts a corresponding fixed point on the road.
They are relatively at rest, by definition. Do you deny this?

Hence, no relative motion, how does the bike proceed? That's
the challenge for the student.

> To keep it simple, we would make use of the rotational symmetry of the
> situation and define the position of the wheel relative to the road by the
> horizontal position of its center of rotation. Certainly you can see that
> then the position of the wheel, if it is rolling on the road, changes
> relative to the road insofar as that it changes relative to a fixed point on
> the road.

um yes, the bicycle achieves forward motion. I don't think
there's any dispute about that.

If you want to define "position of the wheel" (or position of the bike)
as the axle's position relative to the road, that's sensible.

> And even if you do not agree with that choice, certainly you can see that a
> fixed point on the rubber of the wheel is in a continuous, oscillating
> motion relative to (any point on) the road.

Not when we focus on those points along the track!
You miss the point of the paradox completely.

>> But it's a wheel, hence achieves continuous forward motion.
>
> Because there is friction between it and the road and (ideally) it does NOT
> slide at all.

Right. Which contradicts your statements above.

Now, try this pop quiz:
Consider a point P on the tire. It drops and hits the
pavement, the leading edge of the track. It then moves
along the track. Very simple.

A fly lands on P, at the leading edge, and free rides for a
second. He looks across the street, sees a house. Consider
his frame at rest. Does he see the house move, during his ride?

--
Rich

On April 15, Michael Moroney wrote:
> On 4/15/2022, Odd Bodkin wrote:
>> The wheel cannot *accelerate* without the application of friction force
>> between the tire patch and the road.
>> The wheel can “progress” at constant speed with or without friction.
>> Anybody who has rolled a smooth, hard ball on smooth ice knows that the
>> ball will “progress”
>> If a wheel has tangential speed v, this *means* that relative to the center
>> of the wheel the top of the wheel has speed v in one direction,
>> Now map that with a Galilean transform to a frame
>> To first order, the deformation of the tire doesn’t affect the friction at all.
>
> Although it may seem contradictory, the patch of
> the tire has static friction with the road. This is because the patch
> is stationary relative to the road.

Quite.
The tire moves due to the static coefficient friction. No
different than pushing with the sole of your shoe.

Notice that this trivial observation is typical of Bod. He's
such a scatterbrain, he never offers anything other than
the laughably wrong, or trivially true.

He dredges up random jargon and memories of 11th grade
physics (one of his obsessions), mashes them, tosses them
into the stew, and believes he's contributed to the meal.

I wouldn't say he makes too many errors to bother correcting.
Rather, his brain fragments like Humpty Dumpty, one can't put
him back together.

Look at the stuff quoted above:
Galilean transform;
static and rolling resistance;
ice is frictionless (who woulda thunk?)
the wheel has tangential speed, relative to the axle;
the bike moves forward;
when the wheel starts moving, it accelerates, wow!

And - of course - not one of these 'thoughts' address
the question. He set a new standard in this thread, I doubt
he'll ever top it -

--
Rich

RichD wrote:

>>> If a wheel has tangential speed v, this *means* that relative to the
>>> center of the wheel the top of the wheel has speed v in one direction,
>>> Now map that with a Galilean transform to a frame To first order, the
>>> deformation of the tire doesn’t affect the friction at all.
>>
>> Although it may seem contradictory, the patch of the tire has static
>> friction with the road. This is because the patch is stationary
>> relative to the road.
>
> Quite.
> The tire moves due to the static coefficient friction. No different
> than pushing with the sole of your shoe.

all three wrong. The top of the tire has the speed 2v, and ideally there
should be no friction, but static point applied force.