I Rolling Without Slipping

[erobz]

You don't have to believe anything. You can do your own experiments, to check if static friction changes direction, as the solution suggests.

I don't have a PhD...no one will believe me when I tell them I've found the "Golden Wheel". I just have an Bs MET (Mechanical Engineering Technology) from a low rent university. Maybe you can?

 

[jbriggs444]

No my dispute is "where should we stop believing it"

That does not clarify things for me.

Has anyone found a single "Golden Wheel", let alone the practically infinite set of them - there is "apparently" a "Golden Wheel" for every set of parameters we selected.

You are agreeing that for any set of parameters ($M$, $F$, $R$, $\kappa$ there is a $q$ for which $F_s$ vanishes according to the model?

Plot it out on Desmos if you don't believe it. I did.

You are saying that Desmos agrees as well?

I say when the model tells us there is a "Golden Wheel"

You wish to consider a wheel with the requisite $M$, $R$ and $q$ so that $F_s$ goes to zero for a given $\kappa$ to be "Golden" for the given $\kappa$. That is fine. It is just a word. You are free to use it. Though it would be polite to define a word before using it.

we say meh....

Yes indeed.

Meh.

 

[erobz]

You wish to consider a wheel with the requisite $M$, $R$ and $q$ so that $F_s$ goes to zero for a given $\kappa$ to be "Golden" for the given $\kappa$. That is fine. It is just a word. You are free to use it. Though it would be polite to define a word before using it.

"Golden Wheel": A wheel of parameters $R_1,R_2,q,\kappa$ that accelerates - executing rolling without slipping on every surface without applying a frictional force to any of said surfaces. Its what we've been talking about this whole time.

 

[jbriggs444]

"Golden Wheel": A wheel of parameters $R_1,R_2,q,\kappa$ that accelerates - executing rolling without slipping on every surface without applying a frictional force to any of said surfaces.

And you will not settle for negligible frictional force? You want it to be exactly zero frictional force and exactly zero slippage regardless of rolling resistance?

Nobody is claiming that a physical Golden Wheel exists. That is a claim that you have invented yourself.

The reasonable claim is simpler. We can design a wheel to have negligible static friction and negligible slippage regardless of the reasonable surface on which it is placed. "Reasonable" means that you are not allowed to use things like mud, sand or fly paper.

You tell us how negligible you want the difference between the physical behavior and the model and we can tell you how reasonable we need the surface and wheel to be.

 

[erobz]

Nobody is claiming that a physical Golden Wheel exists. That is a claim that you have invented yourself.

I have not invented anything of the sort...the mathematics invented it. I'm just giving it the flippant name it deserves when I call it "The Golden Wheel" given everything what has been discussed on a profound creation of a universal key for all locks.

 

[A.T.]

"Golden Wheel": A wheel of parameters $R_1,R_2,q,\kappa$ that accelerates - executing rolling without slipping on every surface without applying a frictional force to any of said surfaces.

In reality any measurement has limited accuracy, and anything you measure is subject to noise. Expecting to reliably measure any exact value of friction (not just zero) is silly.

But someone with an B.S. in engineering should be easily able to do an experiment, that checks if the friction has different direction, for the predicted combinations of the above parameters.

 

[erobz]

But someone with an B.S. in engineering should be easily able to do an experiment, that checks if the friction has different direction, for the predicted combinations of the above parameters.

I think "easily" is a relative term.

I never said I was a good engineer. I'm a stay at home dad, I mostly just clean stuff and help my kids with homework and take them to sports/arts/girl scouts/ etc...

You guys probably have all the stuff laying around from your demos on the subject.

 

[A.T.]

... on every surface ...

That part is also wrong. If the problem doesn't say anything about rolling resistance, then it's implied to be negligible, which excludes a lot of surfaces.

 

[PeterDonis]

I don't like it when people tell me (who I feel\think are my teachers) "It's obvious that ...yada yada". I have a bit of a problem with authority; a chip on my shoulder from past experiences with that phrase.

Please note that these comments are irrelevant to the topic.

 

[PeterDonis]

This thread has run its course and is now closed. Thanks to all who participated.