[alancalverd]

Re "How?"
like this.

Oh dear, I fear you have opened the floodgates to a diatribe against the Kibble Balance, CGPM, SI and the entire edifice of metrology!

[Bored chemist]

Re "How?"
like this.

Oh dear, I fear you have opened the floodgates to a diatribe against the Kibble Balance, CGPM, SI and the entire edifice of metrology!

The Kibble balance is sufficiently clever that it can stand up for itself.

And the use of "nulling" methods also ticks that box.
https://nvlpubs.nist.gov/nistpubs/ScientificPapers/nbsscientificpaper349vol15p325_A2b.pdf
https://byjus.com/jee/potentiometer/
https://en.wikipedia.org/wiki/Operational_amplifier
https://en.wikipedia.org/wiki/Polarimeter#Laurent's_half-shade_polarimeter

It's remarkable that our friend Hamdani seems to think I will have some sort of difficulty backing up my claims

[alancalverd]

None of which will deter Hamdani.

[hamdani yusuf (OP)]

Re "Here's another example to show that expected rotational radius "
That depends whether or not you are sensible in your expectations.
If you are not, that isn't our responsibility.
This "The question is, what's the torque produced by the force?" is a meaningless question.
It's like asking "How far is it to Rome?". There is no "right" answer.

If you don't specify "about such and such a point" then you can't sensibly ask what the torque is.

Pissing about with the units does not alter that.



And, if I have measured the length of the green line in this picture correctly, the answer is about 0.55 N m

Diag 2.png (15.27 kB . 722x588 - viewed 484 times)

Why did you rotate the drawing? It makes less physical sense. Where is the axis of rotation?

[hamdani yusuf (OP)]

Re "How?"
like this.
The feedback system ensures that the torque exerted by the weight is countered by that produced electromagnetically, and the needle stays in the same place.
Interestingly, his system would be improved greatly by cutting the bottom of the "flag" that shuts of the light at an angle. That way, there would be a small but definite "linear" range over which the light is (roughly) proportional to the angular displacement.


It possible to replace the simple electronics with and A to D converter, a computer, and a D to A converter.
You can then programme the computer to produce any feedback function you chose, including one which is "slightly more than proportional" resulting in the needle actually rising slightly under load.
You could produce a system with an apparent negative stiffness.
This invalidates your assertion about "The finite rigidity of the materials"

For extra marks, try to think of why it would be sensible to introduce such a non-linearity.

It seems to me like you haven't watched the video carefully, or you don't understand how the device that he built works. So, pay attention on the function of photodiode there.

[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.

There are many equations relating torque to other physical quantities. But one of them is preferred by most people, especially in ancient times, to determine its standard unit, which is force times rotational radius. It's understandable  because they are relatively easier to measure, compared to other quantities like rotational inertia, angular momentum, angular velocity, angular acceleration, work, and power.

Moreover, the rotational radius can be considered constant in many situations. But that's not necessarily the case in orbital mechanics, as shown in the article above, where it generally changes over time. In a stable orbit where external forces are negligible, the angular momentum is conserved. Torque is the physical quantity which determines the rate of change of the angular momentum.

Some visualizations might help us understand the problem better.
https://en.wikipedia.org/wiki/Kepler%27s_laws_of_planetary_motion

Kepler's first law placing the Sun at one of the foci of an elliptical orbit


Heliocentric coordinate system (r, θ) for ellipse. Also shown are: semi-major axis a, semi-minor axis b and semi-latus rectum p; center of ellipse and its two foci marked by large dots. For θ = 0?, r = rmin and for θ = 180?, r = rmax.


The same (blue) area is swept out in a fixed time period. The green arrow is velocity. The purple arrow directed towards the Sun is the acceleration. The other two purple arrows are acceleration components parallel and perpendicular to the velocity.



Planet orbiting the Sun in a circular orbit (e=0.0)

Planet orbiting the Sun in an orbit with e=0.5
The red ray rotates at a constant angular velocity and with the same orbital time period as the planet, T=1.
S: Sun at the primary focus, C: Centre of ellipse, S': The secondary focus. In each case, the area of all sectors depicted is identical.

In this cases, net torque is zero because the force is directed toward the axis of rotation, which does not necessarily coincide with the geometrical center of the orbital trajectory. There is no change in angular momentum of the system. There is no change in total mechanical energy either (kinetic + potential).

Note that an ellipse has two foci which are geometrically identical. Only one of them is the center of planetary orbit. This can be seen as a more reason to distinguish between geometric radius and rotational radius, and reflect the difference in their respective units.

[hamdani yusuf (OP)]

Meta's AI isn't smart enough

Then why the F*&^*^ did you use it?

That's what I keep asking.
Why use AI which can not be relied on to answer simple questions?
It hardly matters that it can't count the Rs in a word. We know the right answer to that, and we can all laugh at it.

But if you ask it a question to which you do not know the answer, you don't know if it gets it right or not.
(I hesitate to say this  but it's like asking the Bible for moral advice then, when it tells you slavery is a good thing, you dismiss that as metaphorical. You can only do that because you already know slavery is wrong).

If you need to know the answer in advance in order to check if the AI can answer it, then there's no point asking teh AI, is there?

When someone isn't smart enough, they can refer to someone else which is smarter. Meta AI gave reference to an article.

It also gave another link, but it contains the same information as previous link. https://www.researchgate.net/publication/357717817_Improved_Units_of_Measure_in_Rotational_Mechanics

ChatGPT 4o and Gemini Flash 2.0 are smarter, and they offered some solutions. But they didn't give reference.

By comparing different answers from different AI models, we can get more complete information on the subject of discussion and reveal our current blindspots.

[hamdani yusuf (OP)]

Hamdani: You are wasted here!

Your inability to understand simple physics, coupled with your inability to answer a question, and your inability to admit that you are wrong, makes you better qualified for high political office than anyone else on the planet.

I will be pleased to recommend you for an initial post as Minister for Education, for which you do not actually need to be elected. When you have completely obfuscated the national curriculum, I am sure one or other bunch of incompetent parasites will be pleased to find you a safe parliamentary seat from which you can happily talk bollocks into the TV cameras until you have earned an inflation-proofed pension and several influential directorships of companies that sell bullshit to the unwary.

It has been a pleasure to know you.

Here's another example to show that expected rotational radius is not always the same as the real rotational radius.
It's similar to previous case, but this time a solid object is obstructing the rotation.
The question is, what's the torque produced by the force?

It seems like the question is too hard to answer. So I add some information in the diagram.


The wrench doesn't accelerate, thus the net force acting on it must be zero.
The wrench doesn't change its rotation rate, thus the net torque acting on it must be zero.

[hamdani yusuf (OP)]

I asked Grok 3, Can we improve the standard units of rotational quantities?

The standard units for rotational quantities?radians for angles, radians per second for angular velocity, and radians per second squared for angular acceleration?are mathematically consistent and widely adopted, but they can be unintuitive for practical applications or public understanding. Here?s an analysis of potential improvements, balancing mathematical rigor, usability, and convention:
Current Units and Their Strengths
Angle: Radian 
Dimensionless (ratio of arc length to radius), simplifies equations in physics (e.g., s=rθ).

Naturally arises in calculus (e.g., derivative of sin⁡(θ)\sin(\theta)\sin(\theta)
 is clean in radians).

Universal in scientific contexts.

Angular Velocity: Radians per second (rad/s) 
Ties directly to linear velocity via v=rω
.

Consistent with radian-based equations.

Angular Acceleration: Radians per second squared (rad/s?) 
Follows naturally from angular velocity.

Torque: Newton-meters (N?m) 
Consistent with force ? distance, integrates well with linear mechanics.

Moment of Inertia: Kilogram-meters squared (kg?m?) 
Aligns with mass and distance, works in equations like τ=Iα.

Issues with Current Units
Radians are abstract: 
Unlike degrees (based on a full circle = 360?), radians (≈57.3? per radian) feel less intuitive for non-experts or practical fields like engineering and navigation.

Dimensionless nature can confuse students learning dimensional analysis.

Disconnect in everyday use: 
Rotational frequency is often measured in revolutions per minute (RPM) in engineering (e.g., engines), requiring conversion to rad/s for physics.

Public contexts (e.g., machinery specs) rarely use radians.

Torque vs. Energy: 
Torque (N?m) and energy (joules, also N?m) share units, which can confuse learners despite their distinct physical meanings (vector vs. scalar).

Complexity in education: 
Students often struggle with radians due to their mathematical origin, delaying fluency in rotational dynamics.

Proposed Improvements
Alternative Angle Unit: Gradians or Turns 
Gradian (grad): 400 grads = 1 full circle, 1 grad ≈ 0.9?. Used in some engineering contexts (e.g., surveying). 
Pros: Divides circle into 100/400, aligns with metric system?s base-10 preference. 

Cons: Less intuitive than degrees, not widely adopted in physics, still requires conversion for calculus (radians remain superior here).

Turn (or revolution): 1 turn = 1 full rotation (2π radians). 
Pros: Intuitive for cyclic processes (e.g., wheels, motors). Directly maps to RPM (1 RPM = 1/60 turns/s). 

Cons: Large unit for small angles; less precise for mathematical work unless subdivided (e.g., milliturns). 

Use Case: Define angular velocity as ?turns per second? (e.g., 1 turn/s = 2π rad/s) for engineering or public contexts.

Standardize Rotational Frequency (Hz or RPM) 
Define rotational frequency in hertz (Hz) (cycles per second) or RPM for practical applications. 
Example: A motor at 1800 RPM = 30 Hz = 188.5 rad/s. 

Pros: Hz aligns with SI units for frequency; RPM is industry-standard. 

Cons: Requires conversion to rad/s for torque or dynamics calculations. 

Proposal: Use Hz for rotational frequency in specs, with rad/s reserved for physics equations.

Distinct Torque Unit 
Introduce a unique unit for torque to differentiate from energy (joules). 
Example: Call torque ?newton-meter-torque? (N?m_t) or a new name (e.g., ?torqon?). 

Pros: Clarifies vector (torque) vs. scalar (energy) distinction. 

Cons: Adds complexity, breaks with current SI consistency. 

Alternative: Emphasize context in education (e.g., torque as N?m in rotational equations, joules for work).

Intuitive Subdivisions for Radians 
Introduce named subdivisions of radians for small angles, akin to degrees? minutes and seconds. 
Example: 1 radian = 100 ?centirads? (1 centirad ≈ 0.573?). 

Pros: Bridges gap between radians and degrees for practical use. 

Cons: Adds nomenclature complexity; may not gain traction in pure math.

Unified Rotational Framework 
Create a parallel system for rotational quantities optimized for engineering/public use: 
Angle: Turns or degrees. 

Angular velocity: Turns per second or RPM. 

Angular acceleration: Turns per second squared. 

Torque: Retain N?m but clarify context.

Keep radians for theoretical physics and calculus-heavy contexts. 

Pros: Dual system caters to different audiences (scientists vs. engineers). 

Cons: Risks confusion if conversion isn?t seamless; adoption would be slow.

Practical Challenges to Change
Global Adoption: SI units are entrenched; changing them requires international consensus (e.g., via BIPM). 

Education: Curricula would need overhaul to teach new units or dual systems. 

Industry: Engineering standards (e.g., automotive, aerospace) rely on RPM and degrees; shifting to turns or gradians would face resistance. 

Mathematical Purity: Radians are deeply embedded in physics and math (e.g., Euler?s formula, Taylor series); alternatives like turns complicate these.

Recommendation
Rather than overhaul SI units, enhance their usability:
Promote ?turns? as a secondary unit for angles and angular velocity in engineering and education. Standardize conversions (1 turn = 2π rad) in software and textbooks. 

Encourage Hz or RPM for rotational frequency in specs, with rad/s as the bridge to physics. 

Improve education: Teach radians alongside degrees early, emphasizing their role in simplifying physics. Use analogies (e.g., ?radians measure arc length in radius units?). 

Clarify torque vs. energy in teaching and documentation, possibly via notation (e.g., N?m for torque, J for energy).

This approach preserves the mathematical elegance of radians while making rotational quantities more accessible for practical and educational contexts. A full transition to new units like gradians or turns is unlikely due to inertia in standards, but a dual-system approach could bridge the gap.

Previously, it has different answer, where it doesn't recognize the problems in current standards. Although, when its thought process was revealed, it seems to be aware of the problems, but it decided to suppress them in its final answer.

[Bored chemist]

"When someone isn't smart enough, they can refer to someone else which is smarter."
Yes.
So I will modify my question.
My question is "are you not smart enough to count the Rs in strawberry?"

If you were looking for a reference why not use a search engine?
A search for "better units for measuring rotational quantities" using google got the AI response which includes
"Consistency with SI Units:
Radians are a dimensionless unit (they are a ratio of two lengths), which makes them compatible with the International System of Units (SI) and helps to avoid errors in calculations. ".

But if you ignore the AI hallucination and look at  the search result, you get (as the top result) the same paper which you cited.

Now I can read the paper and look at the author's reasoning and make a decision about whether or not that proposed change is worth making.
I'm inclined to leave things alone- the system has worked for hundreds of years. But that's a judgement call.I'm not happy to leave a computer to deal with things that are a matter of opinion.


As for your question with the picture of a wrench...
It wasn't too hard to answer.
I answerwed it.

It was poorly specified.
But you are being inconsistent.

When the force is applied the wrench will, in fact, turn.
Don't you remember telling me that
"The finite rigidity of the materials guarantee that the rotational angle will not be zero when a force is applied at some distance away from the supporting bolts not exactly directed at the bolt itself, before it produces reactionary force to cancel the motion."?

But, this is physics.
We can pretend that the wrench is infinitely rigid.
In that case there is no movement.

If we look at the paper you referred us to it says "NI units assign to radius should have units meter/radian because radius is a conversion factor between angular size and circumferential length, as in arclength = r θ. "

Well, if theta is zero, the circumferential length is also zero.
Nothing rotates.
We don't have a situation where NI would be useful because ", the author recommends retaining SI units as they are and informing users who want correct units that NI units solve the technical problems of SI units".

However, as I illustrated, and Galileo allegedly said "And yet, it turns".

[hamdani yusuf (OP)]

When the wrench already stopped turning, the total torque is zero. This statement should be obvious.
If the obstructing object has a finite stiffness, like all physical objects do, then some displacement will be propagated to the bolt. In turn, the thread on the bolt will generate reactionary force proportional to the rotational displacement. After a brief deceleration, the rotation will stop and the total force as well as torque are zero.

[hamdani yusuf (OP)]

Both I and RJ Petti have identified that rotational radius is better expressed in arc length displacement per rotational angle. His proposed solution is to split the whole unit system by creating a new one especially for rotational mechanics. My own solution is much simpler, which is distinguishing rotational radius from geometric radius, and assign different units for them. While geometric radius keeps its current unit, the same as length, rotational radius should be expressed in length per angle, because it's derived from arc length divided by angle.

[alancalverd]

When the wrench already stopped turning, the total torque is zero.

Utter drivel. It would be zero in your units, but that would imply that tightening a nut has no purpose since the torque was zero before you did anything.

Do you work for Boeing quality control?

[hamdani yusuf (OP)]

When the wrench already stopped turning, the total torque is zero.

Utter drivel. It would be zero in your units, but that would imply that tightening a nut has no purpose since the torque was zero before you did anything.

Do you work for Boeing quality control?

What is it in your unit?
How do you interpret the word "total"?

[hamdani yusuf (OP)]

When the wrench already stopped turning, the total torque is zero. This statement should be obvious.
If the obstructing object has a finite stiffness, like all physical objects do, then some displacement will be propagated to the bolt. In turn, the thread on the bolt will generate reactionary force proportional to the rotational displacement. After a brief deceleration, the rotation will stop and the total force as well as torque are zero.

In the case where 1 Newton force is applied at 1 meter away from the axis of rotation, and the bolt radius is 10 mm, the thread needs to produce 100 Newton force to cancel out the torque and prevent the bolt from turning. If the friction force by the thread is less than 100 Newton, the bolt will be accelerated rotationally.

When there is no object obstructing the wrench, the cancelling torque is produced by the thread of the bolt and nut. But with obstructing object preventing propagation of force to the bolt, the cancelling torque is produced by the normal force of said object. The thread doesn't produce cancelling torque.

[paul cotter]

There is no cancellation of torque when an object fails to turn, there is just insufficient torque to produce rotation. Similarly when one pushes against a wall, the wall does not move but the force is still there.

[hamdani yusuf (OP)]

There is no cancellation of torque when an object fails to turn, there is just insufficient torque to produce rotation. Similarly when one pushes against a wall, the wall does not move but the force is still there.

Read again Newton's laws of motion.

[paul cotter]

On the contrary you need to learn some BASIC mechanics.

[alancalverd]

What is it in your unit?

Whatever the torque wrench indicates.

[alancalverd]

In the case where 1 Newton force is applied at 1 meter away from the axis of rotation, and the bolt radius is 10 mm, the thread needs to produce 100 Newton force to cancel out the torque and prevent the bolt from turning. If the friction force by the thread is less than 100 Newton, the bolt will be accelerated rotationally.

So a lubricated bolt can't be tightened to a set torque, everything in my car maintenance manual is wrong, and the wheels will fall off unless I use rusty bolts. I learn something new every day.