[alancalverd]

However, the elliptical path ensures that the planet's distance from the Sun varies, which ties into the second law.

This is the kind of misleading bullshit you get from a chatbot. Science is doomed.

[hamdani yusuf (OP)]

Rotational radius equals derivative of rotational displacement with respect to rotational angle.

In the case of a parking brake, there is no rotation, so δs/δθ is undefined.

Then the torque is undefined.

[hamdani yusuf (OP)]

Hi ES. We all make mistakes and I certainly have had to be corrected on many occasions but I cannot recall any of yours apart from typos. Hamdani is seemingly incapable of error and I have never met anyone with such dogged intransigence to learning. When proven wrong he digresses and obfuscates. I have repeatedly said that I am finished dealing with such exasperation but I am drawn back when I see blatant error that may mislead the general reader.

Which one is the biggest error that you find in my tables?

[hamdani yusuf (OP)]

Hi.

.... so everyone else who read this thread can learn...   

    I genuinely don't like upsetting people.  I've written a few forum posts myself that weren't well recieved and I've just had to move on.   The forum is useful for discussion and sometimes I / we  just won't like the replies.  Sometimes I've had to recognise that my own ideas had some flaws and sometimes I've just worked through the problems again and become more convinced they may be right while the replies were wrong.  The thing is, forum moderators and other regular forum users are just human in the same way that you are just human.   Most of us are just doing our best.

    It may be you're absolutely correct,  I haven't read all of it so I don't know.   It's just that with this many pages, no-one else is ever going to want to read it.

   Sorry.  I really am sorry.   Typically a forum is only useful for the original poster and a handful of people to learn and especially to discuss something.   This forum does not work as a platform to teach the entire world and I doubt that the original aims, or terms of use, for this forum would want people to use it in that way.

       Extract from the Forum Acceptable Usage Policy,   available at   https://www.thenakedscientists.com/forum/index.php?topic=8535.0
      The site is not for evangelising your own pet theory.  It is perfectly acceptable that you should post your own theory up for discussion, but if all you want to do is promote your own idea and are not inviting critical debate about it, then that will not be acceptable.

      Once again, I am genuinely sorry that the forum isn't providing the service or facillities you are seeking.   That may be a failing on   our / their   part but it just is what it is.   It may be that you have got all that you can get out of this forum.   If you're sure your idea is a golden one, then you could always find another way to promote it and bring it to public attention.   For example, take it to a university and propose these ideas as something you would like to research and hopefully publish.   It may cost you money in course fees and it will take you some time but if you're driven enough to let the world know about your idea then be positive, "pro-active", "fully committed" and find a way to make something like that happen.

   Good Luck and, as always, please be assured of my best wishes towards you.

Internet, social media, and AI have and will democratize ideas, information and knowledge. They are memes that will have to compete with one another for their own existence in a virtual universe. My tables have shown that the proposed new standard units of rotational quantities are more consistent than current standard. If more people have the opportunity to look into them, those new standard will have a better chance to compete in a more equal footing.

[alancalverd]

Rotational radius equals derivative of rotational displacement with respect to rotational angle.

In the case of a parking brake, there is no rotation, so δs/δθ is undefined.

Then the torque is undefined.

Which shows the weakness in your redefinition of torque! There is obviously a torque from the weight of the vehicle trying to make the wheel rotate, and thus we need to apply a counter torque from the brake pad and disc to prevent it rotating. It is ESSENTIAL that we calculate the required counter torque, to prevent death and destruction.

[hamdani yusuf (OP)]

Rotational radius equals derivative of rotational displacement with respect to rotational angle.

In the case of a parking brake, there is no rotation, so δs/δθ is undefined.

Then the torque is undefined.

Which shows the weakness in your redefinition of torque! There is obviously a torque from the weight of the vehicle trying to make the wheel rotate, and thus we need to apply a counter torque from the brake pad and disc to prevent it rotating. It is ESSENTIAL that we calculate the required counter torque, to prevent death and destruction.

What you think is obvious may turn out to be false. It's shown in the case of rolling car, where the whole car is rolling instead of the wheels only.
When the axis of rotation cannot be determined, the radius of rotation cannot be determined either, which makes the torque cannot be determined. Saying otherwise would be hallucinating.

[alancalverd]

If you can't solve  the problem of braking on a stationary car, your definition of torque is useless. Everyone else's definition works perfectly.  There is nothing more to be said.

[paul cotter]

Agreed, Alan, this thread is utterly pointless and a waste of forum resources.

[hamdani yusuf (OP)]

If you can't solve  the problem of braking on a stationary car, your definition of torque is useless. Everyone else's definition works perfectly.  There is nothing more to be said.

What's your definition?

[alancalverd]

A force that tends to cause or prevent rotation.

τ = F.r where r is the distance from the point of application of the force to the axis of actual or potential rotation

[hamdani yusuf (OP)]

Rotational radius equals derivative of rotational displacement with respect to rotational angle.

In the case of a parking brake, there is no rotation, so δs/δθ is undefined.

Then the torque is undefined.

Which shows the weakness in your redefinition of torque! There is obviously a torque from the weight of the vehicle trying to make the wheel rotate, and thus we need to apply a counter torque from the brake pad and disc to prevent it rotating. It is ESSENTIAL that we calculate the required counter torque, to prevent death and destruction.

What you think is obvious may turn out to be false. It's shown in the case of rolling car, where the whole car is rolling instead of the wheels only.
When the axis of rotation cannot be determined, the radius of rotation cannot be determined either, which makes the torque cannot be determined. Saying otherwise would be hallucinating.

When you are hallucinating, what you see may look obvious. What you hear may sound obvious. But they don't necessarily represent physical reality.

[hamdani yusuf (OP)]

A force that tends to cause or prevent rotation.

τ = F.r where r is the distance from the point of application of the force to the axis of actual or potential rotation

Which one will you choose, if the axis of actual rotation is different from the potential rotation? What if there are more than one potential rotation?

[alancalverd]

It's up to you. If the brake disc has a flaw, and the crack propagates, the axis of potential rotation of the broken bit will be closer to the pad than the geometric center of subsequent actual rotation of the rest of the wheel. Whether the crack propagates depends on the static torque.

[hamdani yusuf (OP)]

The new standard can also have the same benefit of brevity as option 0. Like the unit for power, which we usually state in Watt instead of Newton meter per second, we can introduce a new unit equals to Newton meter per radian.
What would it be? Here are some options.
Wenn
Woo
Wyy
Werr
You might see a pattern here.

Alternatively, we can use someone's name with significant contributions to the understanding of torque. According to various AI models, they are:
Archimedes
da Vinci
Newton
Leibniz
Euler
d'Alembert
Lagrange
Hamilton
Poisson
Thomson
Thompson

Various AI models consistently mentioned Archimedes as the earliest contributor to the concept of torque.

Archimedes explained the principle of leverage, which is closely related to torque. He understood that:

- The force applied to a lever, multiplied by the distance from the fulcrum (pivot point), determines the rotational force (torque).
- The ratio of the distances from the fulcrum to the points where the forces are applied determines the mechanical advantage of the lever.

In other words, Archimedes discovered that:

Torque = Force ? Distance

This fundamental principle is still widely used today in mechanics, engineering, and physics to calculate torque and understand rotational motion.

Archimedes' work on levers and torque was presented in his book "On the Equilibrium of Planes," which is considered one of the greatest works of ancient Greek mathematics and engineering.

There is no evidence that Archimedes mentioned a specific unit for torque.

In fact, the concept of torque as we understand it today, with its associated units, developed much later.

Archimedes did discuss the principles of leverage and rotational motion, but he didn't use the same mathematical framework or units that we use today to describe torque.

Meta AI

Unfortunately his explanation is limited to the concept of leverage or mechanical advantage, and didn't cover the whole range of modern understanding of torque and its relationship with other rotational quantities.

His practical approach was useful for some applications, thanks to its simplicity. But when it's used more generally to describe other rotational quantities such as rotational inertia, angular velocity, angular momentum, angular acceleration, rotational kinetic energy and power, we get inconsistency in their units. A rotational quantity can get different standard units if they were derived using different equations.

To be fair, it's not Archimedes' fault that caused this confusion. He only showed the equation, without mentioning the unit for torque. The unit for torque was set much later by people who developed the concept further. It's unfortunate that they naively used Archimedes' equation for torque to determine its unit without considering the types of its operands, as well as its implications to the units of other rotational quantities.

Archimedes' concept of leverage is indeed closely related to torque. But it's not exactly the same as modern concept of torque itself. It depends on the existence of fulcrum, which is basically a mechanical anchorage to an extremely massive object like the earth, which would make the point stationary while the lever is rotating. If the base is light weight objects, they will be moved by the force acted on the lever, which makes the rotational axis change its position during the rotation. In my previous example, the workbench sat on a small boat floating on water.
This fulcrum can also be the contact between two linked levers like scissors and wire cutters.

[hamdani yusuf (OP)]

https://farside.ph.utexas.edu/teaching/301/lectures/node155.html

h = l/m
Clearly, h represents the angular momentum (per unit mass) of our planet around the Sun. Angular momentum is conserved (i.e., h is constant) because the force of gravitational attraction between the planet and the Sun exerts zero torque on the planet. (Recall, from Sect. 9, that torque is the rate of change of angular momentum.) The torque is zero because the gravitational force is radial in nature: i.e., its line of action passes through the Sun, and so its associated lever arm is of length zero.

We can't blame ancient people for not understanding the concept of rate of change, nor angular momentum. It's okay for them to try to define torque using simpler concepts which were easier to understand.

But now that most of us have already understood those concepts. Thus the modern definition of torque shouldn't be difficult to explain, at least to those with a decent scientific knowledge.

The reason for choosing a standard is to have a better consistency. Which is exactly what the proposed new standard units of rotational quantities have shown, compared to currently existing standard.

[paul cotter]

Those "ancient people" had a far better understanding of torque than you. Torque IS a simple concept to everyone except you, without the need of differential calculus.

[alancalverd]

Those ancient people who used spinning wheels, spinning tops, and suchlike, were fully cognisant of the conservation of angular momentum.

The folk who made spoked cart wheels (2000 BC) understood torque, as did the users of the Archimedian screw (1000 BC, before Archimedes!) the windlass (ascribed to Archimedes but surely of earlier origin) and the screw wine press (100 AD)

Interestingly, whilst it is clear that the concepts of differentials and divisions of a circle were well known by 300 BC (arguably earlier but documentation is lacking), it seems that nobody proposed redefining force x distance as  force x distance /angle until a few weeks ago, and nobody has found an excuse for doing so.

Parking brakes, as distinct from scotch ramps, have been in use at least as long as the windlass and windmill, so the calculation of brake force has been done very successfully for thousands of years thanks to everyone's thorough understanding of torque.

[hamdani yusuf (OP)]

Those "ancient people" had a far better understanding of torque than you. Torque IS a simple concept to everyone except you, without the need of differential calculus.

Do you understand the concepts of rate of change? What about angular momentum?
As the name suggests, the modern concept of torque was not recognized by ancient people.

[hamdani yusuf (OP)]

It's up to you. If the brake disc has a flaw, and the crack propagates, the axis of potential rotation of the broken bit will be closer to the pad than the geometric center of subsequent actual rotation of the rest of the wheel. Whether the crack propagates depends on the static torque.

You explicitly admit that it's undetermined until the system actually rotate. Your denials in other posts only show your cognitive dissonance.

[hamdani yusuf (OP)]

Interestingly, whilst it is clear that the concepts of differentials and divisions of a circle were well known by 300 BC (arguably earlier but documentation is lacking), it seems that nobody proposed redefining force x distance as  force x distance /angle until a few weeks ago, and nobody has found an excuse for doing so.

The wiki article below says that someone else had proposed the same thing at least since 1936. May be you hadn't been born yet, so you don't know it.

https://en.wikipedia.org/wiki/Angle#Dimensional_analysis
Plane angle may be defined as θ = s/r, where θ is the magnitude in radians of the subtended angle, s is circular arc length, and r is radius. One radian corresponds to the angle for which s = r, hence 1 radian = 1 m/m = 1.[9] However, rad is only to be used to express angles, not to express ratios of lengths in general.[7] A similar calculation using the area of a circular sector θ = 2A/r2 gives 1 radian as 1 m2/m2 = 1.[10] The key fact is that the radian is a dimensionless unit equal to 1. In SI 2019, the SI radian is defined accordingly as 1 rad = 1.[11] It is a long-established practice in mathematics and across all areas of science to make use of rad = 1.[4][12]

Giacomo Prando writes "the current state of affairs leads inevitably to ghostly appearances and disappearances of the radian in the dimensional analysis of physical equations".[13] For example, an object hanging by a string from a pulley will rise or drop by y = rθ centimetres, where r is the magnitude of the radius of the pulley in centimetres and θ is the magnitude of the angle through which the pulley turns in radians. When multiplying r by θ, the unit radian does not appear in the product, nor does the unit centimetre?because both factors are magnitudes (numbers). Similarly in the formula for the angular velocity of a rolling wheel, ω = v/r, radians appear in the units of ω but not on the right hand side.[14] Anthony French calls this phenomenon "a perennial problem in the teaching of mechanics".[15] Oberhofer says that the typical advice of ignoring radians during dimensional analysis and adding or removing radians in units according to convention and contextual knowledge is "pedagogically unsatisfying".[16]

In 1993 the American Association of Physics Teachers Metric Committee specified that the radian should explicitly appear in quantities only when different numerical values would be obtained when other angle measures were used, such as in the quantities of angle measure (rad), angular speed (rad/s), angular acceleration (rad/s2), and torsional stiffness (N⋅m/rad), and not in the quantities of torque (N⋅m) and angular momentum (kg⋅m2/s).[17]

At least a dozen scientists between 1936 and 2022 have made proposals to treat the radian as a base unit of measurement for a base quantity (and dimension) of "plane angle".[18][19][20] Quincey's review of proposals outlines two classes of proposal. The first option changes the unit of a radius to meters per radian, but this is incompatible with dimensional analysis for the area of a circle, πr2. The other option is to introduce a dimensional constant. According to Quincey this approach is "logically rigorous" compared to SI, but requires "the modification of many familiar mathematical and physical equations".[21] A dimensional constant for angle is "rather strange" and the difficulty of modifying equations to add the dimensional constant is likely to preclude widespread use.[20]

It's obvious that I'm not the only one who's not satisfied by the current standard units for some rotational quantities for their inconsistencies with each other. The problem has already been identified at least since 1936, although no satisfying solution has been found.
The first option is to change the unit of a radius to meters per radian, but this creates new incompatibility. It was rejected in favor of keeping the old incompatibilities instead. It seems like human thought has its own version of inertia.
These incompatibilities can be eliminated by making a distinction between geometric radius and rotational radius. While geometric radius is still measured in meter, rotational radius is measured in meter per radian because it represents the ratio between arc length of the rotational motion and its angular distance.