[hamdani yusuf (OP)]

In the first picture, the angle indicates the applied torque, i.e. the flexion of the spring steel shaft, not the angle through which the bolt has been rotated.

It indicates the angle between the head and the handle. You are denying your own imagination, instead of my statement.

[alancalverd]

Anyone who has ever seen a flexion torque wrench will know that

the flexion of the spring steel shaft,

is indeed displayed as

the angle between the head and the handle.

though strictly you should have said "between the present position of the handle and a line drawn from the center of the head to the handle when the applied torque is zero" . But that is too obvious for most of us.

[hamdani yusuf (OP)]

In the second picture the head-handle angle remains at  < 30 deg until the applied torque exceeds the preset value, at which point the handle clicks through at least a further 30 degrees. This could be alarming and dangerous in a cramped working environment - my preset "clicker" doesn't have a hexagonal cam, just a single cam and a limit of about 5 degrees.

Don't confuse the torque indicator or limiter with the ratchet mechanism!

The hexagonal head can be replaced with other polygon with more sides so it works with smaller angle.

[alancalverd]

Aha! I've just found a device that does what you say! It's a Straumann dental implant ratchet torque wrench. Very clever, and prevents overtorqueing in a way that can't be achieved with a flexion or single-click device. There's an even neater French device that apparently doesn't require the dentist to ratchet the handle back and forth - even more comfortable for the patient.

[hamdani yusuf (OP)]

A Swift Introduction to Geometric Algebra

This video is an introduction to geometric algebra, a severely underrated mathematical language that can be used to describe almost all of physics.  This video was made as a presentation for my lab that I work in.  While I had the people there foremost in my mind when making this, I realized that this might be useful to the general public, so I also tried to make this useful to others as well.

It briefly describes torque at around 28:00.

[hamdani yusuf (OP)]

How Ratchets Work

We show the details of one of the most common tools used in the garage - the hand ratchet.  We learn how they work by taking apart a common 3/8" ratchet.  Includes closeup/macro views of the inner workings of a ratchet.  We show how the unit functions and then take it apart piece by piece.  Finally, a few quick recommendations on features to look for in a new ratchet - mainly the value of a fine-tooth geared anvil and pawl setup.

[hamdani yusuf (OP)]

The Vector Algebra War

There are a wide variety of different vector formalisms
currently utilized in engineering and physics. For example, Gibbs? three-vectors, Minkowski four-vectors, complex spinors in quantum mechanics, quaternions used to describe rigid body rotations and vectors defined in Clifford geometric algebra. With such a range of vector formalisms in use, it thus appears that there is as yet no general agreement on a vector formalism suitable for science as a whole. This is surprising, in that, one of the primary goals of nineteenth century science was to suitably describe vectors in three-dimensional space. This situation has also had the unfortunate consequence of fragmenting knowledge across many disciplines, and requiring a significant amount of time and effort in learning the various formalisms. We thus historically review the development of our various vector systems and conclude that Clifford?s multivectors best fulfills the goal of describing vectorial quantities in three dimensions and providing a unified vector system for science.

[hamdani yusuf (OP)]

Every Angle Unit Explained in 10 minutes

Timestamps

0:00 Turn
1:24 Degree
3:23 Radian
6:04 Gradian
7:52 Binary Angular Measurement

[hamdani yusuf (OP)]

MIT Physicist Explains Torque As Simply as Possible.

Today we take a very simple approach to explaining what is quite a complex topic, torque!

I commented on the video, which sparked a heated debate with another viewer.

To avoid confusion between unit of torque and energy, torque  can be expressed as Joule per radian. Or Newton meter per radian. Dot product between force and distance produces energy, which is a scalar. Cross product between force and distance from fulcrum produces torque, which is a vector.

This strikes me as an almost surefire way to CREATE confusion and obscure the fundamental nature of torque - which is, as explained clearly in the video,  the product of force times distance (or  as alluded to in the video, more precisely  - the perpendicular component of force times distance).  Using units of torque as Joules per radian makes no physical sense. Joules are the fundamental unit of energy in the SI system, and radians is a (dimensionless) measure of an angle.  What's the angle here that relates to the definition of and understanding of the nature of torque?
When I was a Mechanical Engineering professor, I occasionally heard students use an engineering equation solving program that frequently gave answers in units that made no physical sense.  I created a "wall of shame" at the entrance to my office where everyone entering would immediately see.  If a student lacked the understanding to use appropriate units in the answer to a problem (even if the units "worked out"ok, their solution would find itself on the wall. Most assuredly, Joules per radian would make its way onto the wall. While not quite as egregiously bad, Newton-meter per radian would find itself there as well.  Adding dimensionless numbers as units to perhaps serve as a memory aid is just plain silly.  How about Joules per radian per Re per Fr?  There are a whole host of dimensionless numbers we can choose from, most of which don't add anything meaningful.

If you are confused, that's because you have misunderstood the concept. If the torque doesn't cause change of angular position, no work has been done. You'll understand better if you learn about the torque of a motor. Perhaps experimenting with variable speed drive can help.

I am not the one who is confused here. I perfectly understand that work is forced times distance or,  for a rotational system torque times angle of rotation. My point is that there is no reason to express torque in units of energy per angle of rotation. The fundamental nature of torque is force acting at a distance. Not all torques result in work being done.   Only if the torque is accompanied by a rotation then there is work being done. There is no reason to include the concept of work associated with torque for the situations where there is no work being done.That is, such as the case where the torque is applied statically. Newtons and meters are fundamental units in the SI system. Torque is readily defined in terms of these fundamental units. There is no need to introduce additional units such as radians.
 Furthermore your suggestion that I am confused and my confusion would be cleared up by looking at variables speed devices is quite condescending. I have been engineer for more than 50 years. I worked with and designed vehicle power trains, including those that had continuously variable and infinitely variable speed transmissions. In my work I worked with advanced power trains including those for hybrid vehicles and
I have co-authored numerous SAE papers on the subject, and have taught thousands of Mechanical Engineering students.  I am confident that I am not confused about the fundamental nature of torque.

Torque is the rotational equivalent of force in linear motion. It's a measure of how effectively a force can cause an object to rotate around a specific axis. It's also known as angular force.
Converting linear force into angular force can be done by multiplying it by distance (along the circumference) per angle of rotation.

Based on your  continuing replies, I can only come to the conclusion that you are being deliberately obstinate, or have been poorly educated and don't understand the true nature of torque.  You can search the archives of respectable Engineering publications such as  SAE and ASME, and you will find little, if any at all, evidence to support your position that torque should be expressed as  Joules/radian or Newton meters/rad.

I won't waste any more of my time responding to your comments - and hope that anyone who reads this string of comments is able to understand the problem in using Joules/rad. (Or any other unit of energy/radian  eg calories or BTUs/radian)

The hardest part of learning new things is to first unlearn previous knowledge that is incomplete or inaccurate. It's often easier to teach young people who hasn't been exposed too deep to those previous knowledge.
You can check the unit consistency in motor calculation for power.
P=τ⋅ω
where:
P = Power (Watts, W, Nm/s)
τ = Torque (Newton-meters per radian, Nm/rad)
ω = Angular Speed (radians per second, rad/s)

If you omit the unit radian from torque, you get incorrect unit for power.

[alancalverd]

If you tighten an M8 bolt to 10 Nm and continue to apply 10 Nm, will it turn another radian? No, it won't turn at all.

[hamdani yusuf (OP)]

If you tighten an M8 bolt to 10 Nm and continue to apply 10 Nm, will it turn another radian? No, it won't turn at all.

If its rotation slows down, then the net torque is opposite of the direction of the rotation.
If the rotational speed is constant, the net torque is zero. That includes the condition where it doesn't rotate at all.
Your confusion comes from ignoring reactionary torque by the system.

[hamdani yusuf (OP)]

motor calculation for power.
P=τ⋅ω
where:
P = Power (Watts, W, Nm/s)
τ = Torque (Newton-meters per radian, Nm/rad)
ω = Angular Speed (radians per second, rad/s)

If you omit the unit radian from torque, you get incorrect unit for power.

If you're still struggling to understand my comment above, here's the break down.
Here's a common values in industrial motor.
P = 1000 W = 1000 Nm/s
ω = 3000 rpm = 50 rps ≈ 314 rad/s
τ = P/ω ≈ 1000/314 ≈ 3.18 Nm/rad

You can use an alternative unit, e.g.
τ = P/ω = 1000/50 = 20 Nm/rotation

[hamdani yusuf (OP)]

You can ignore the amount of rotational angle if your application doesn't care about the energy nor the power to produce the required torque. That's usually true if you only have to tighten or loosen bolts and nut. But it can't be generalized to all other use cases.

[hamdani yusuf (OP)]

Here's a common values in industrial motor.
P = 1000 W = 1000 Nm/s
ω = 3000 rpm = 50 rps ≈ 314 rad/s
τ = P/ω ≈ 1000/314 ≈ 3.18 Nm/rad

You can use an alternative unit, e.g.
τ = P/ω = 1000/50 = 20 Nm/rotation

Those values are physically the same magnitude of torque, only expressed in different units. Just like 0 degree Celcius equals 32 degrees Fahrenheit. Or 1 km/s equals 1000 m/s.

[hamdani yusuf (OP)]

I asked several AI chatbots, What's the physical quantity measured in Joule per radian?
ChatGPT, Gemini, Grok, Meta AI, all of them correctly answer that it's torque.

Then I changed the question, What's the physical quantity measured in Joule per rotation? Only Gemini directly answered torque. The others answered it's work, energy, energy per cycle, rotational energy.

Then I asked Gemini What's the physical quantity measured in Joule per cycle?

This is a bit of a tricky one! The physical quantity measured in joules per cycle is energy.
Here's why:
 * Joule is the SI unit of energy. It represents the amount of work done when a force of one Newton displaces an object by one meter in the direction of the force.
 * Cycle refers to a complete sequence of a repeating event, like a wave or an oscillation.
When we talk about joules per cycle, we're essentially describing the amount of energy associated with each repetition of that event. This could be:
 * Energy of a wave: How much energy is carried by each wave cycle.
 * Energy in an oscillation: How much energy is involved in each complete swing of a pendulum, for example.
 * Energy per revolution: In a rotating system, how much energy is transferred or used during each full rotation.
So, while it might seem like a complex unit, joules per cycle ultimately boils down to measuring energy.

[hamdani yusuf (OP)]

I asked Gemini, Don't you think that rotation and cycle means the same thing?

You're right to question that! While the terms are sometimes used interchangeably, there can be a subtle difference between "rotation" and "cycle," especially in scientific contexts.
Here's a breakdown:
 * Rotation: This specifically refers to the spinning motion of an object around its own axis. Think of the Earth rotating on its axis, causing day and night. It emphasizes the physical act of turning.
 * Cycle: This is a more general term that refers to a complete sequence of a repeating event. It can include rotations, but it can also encompass other types of repeating processes, like oscillations (a pendulum swinging back and forth) or even a chemical reaction that goes through a series of steps and then repeats.
Think of it this way:
 * All rotations are cycles, but not all cycles are rotations.
Why the distinction matters:
In physics and engineering, it's important to be precise with language. While "joule per rotation" and "joule per cycle" might sometimes refer to the same thing (especially if the cycle in question is a rotation), using "rotation" specifically emphasizes that we're talking about the energy associated with a turning motion.
In summary:
While often similar, "rotation" is a more specific term that refers to the spinning of an object, whereas "cycle" is a broader term that can include rotations but also other repeating events.

I think it's right. A cycle isn't always a rotation, thus Joule/cycle isn't always express torque, e.g. in linear oscillation, like a spring mass system.

[hamdani yusuf (OP)]

I asked several AI chatbots, What's the physical quantity measured in Joule per radian?
ChatGPT, Gemini, Grok, Meta AI, all of them correctly answer that it's torque.

In hindsight, this should have been obvious, and shouldn't be considered as a new theory.
But somehow many of us have overlooked this concept, including those in the position of authoritative figures.
It seems like once a mistake already became widespread, it's hard to make a correction. At least partially, it's affected by sunk cost fallacy.

[alancalverd]

You could also ask your Artificial Idiot what physical quantity is measured in newton meters.

And what is the name of the unit of one newton meter.

Then ask why it gave the same answer to two different questions.

[hamdani yusuf (OP)]

You could also ask your Artificial Idiot what physical quantity is measured in newton meters.

And what is the name of the unit of one newton meter.

Then ask why it gave the same answer to two different questions.

I asked ChatGPT. what physical quantity is measured in newton meters?

The **Newton meter (N?m)** is a unit of **torque** (or **moment of force**) in the International System of Units (SI). It represents the rotational force applied to an object around an axis. 

Mathematically, **torque (τ)** is given by: 
\[
\tau = r \times F
\]
where: 
- \( \tau \) is the torque in Newton meters (N?m), 
- \( r \) is the perpendicular distance from the axis of rotation to the point where the force is applied (in meters), 
- \( F \) is the force applied (in Newtons). 

Although **work** and **energy** also have the unit **joules (J)**, which is equivalent to N?m, the Newton meter is not commonly used to express energy. Energy is typically written in **joules** to avoid confusion, while torque is always expressed in **Newton meters (N?m)**.

And what is the name of the unit of one newton meter?

The unit Newton meter (N?m) does not have a special name; it is simply referred to as a Newton meter when used to measure torque.

However, when measuring energy or work, 1 Newton meter (N?m) is equivalent to 1 joule (J). The joule is the SI unit of energy, but for clarity, torque is always expressed in Newton meters (N?m) rather than joules.

why torque has the same unit as energy?

Torque and energy both share the unit Newton meter (N?m), but they represent fundamentally different physical concepts. The reason they have the same unit is due to the mathematical definitions of force, distance, and angular motion, but their interpretations are different.

Thus, the confusion seems to have started from removing the unit radian from explicitly stated in the unit of torque. Thus to distinguish between energy and torque when the unit Newton meter is asked, we depend on interpretations.
Having one radian as the angle of rotation, we get convenient result that the arc length equals the radius. But this convenience comes with the cost of ambiguity between two distinct physical quantities.

AI parameters and weights are distillation of internet content. If the internet is already filled with misconceptions, ambiguities, or mistakes, the answers by AI will carry them out to the users. Letting them unaddressed will cause confusions and inefficiency. they can also cause miscommunications and bad decisions.

[hamdani yusuf (OP)]

Here's a common values in industrial motor.
P = 1000 W = 1000 Nm/s
ω = 3000 rpm = 50 rps ≈ 314 rad/s
τ = P/ω ≈ 1000/314 ≈ 3.18 Nm/rad

You can use an alternative unit, e.g.
τ = P/ω = 1000/50 = 20 Nm/rotation

Those values are physically the same magnitude of torque, only expressed in different units. Just like 0 degree Celcius equals 32 degrees Fahrenheit. Or 1 km/s equals 1000 m/s.

When someone says that the applied torque is 3.18 Nm, what they really mean is 3.18 Nm/rad.
It's NOT 3.18 Nm/rotation.
It's NOT 3.18 Nm/degrees.