[paul cotter]

This is my last post on this matter as I have no intention of debating with a dumb computer(s), something that is happening with disconcerting regularity. We were discussing torque, which is a force, NOT a rotation. Rotation may or may not occur but that is a separate issue. This thread will go on and on, to n+1 pages with Hamdani's confusion reigning supreme as more and more extraneous and irrelevant material is used to cloud the concept of torque. As I have said on a different thread  I believe this is just argument for argument's sake with no hope whatsoever of advancement.

[hamdani yusuf (OP)]

Thus demonstrating that ChatGPT is about as much use as Gemini or a chocolate teapot.

What's wrong with its answer? I asked it when people started studying about torque.

[hamdani yusuf (OP)]

We were discussing torque, which is a force, NOT a rotation.

I think you need to first understand what the meaning of a concept as it's currently understood by most of its users.
Only then you can try to find a better alternative to improve the effectiveness and efficiency from current usage.

https://en.wikipedia.org/wiki/Torque
In physics and mechanics, torque is the rotational analogue of linear force.[1] It is also referred to as the moment of force (also abbreviated to moment).

https://en.wikipedia.org/wiki/Force#Second_law
According to the first law, motion at constant speed in a straight line does not need a cause. It is change in motion that requires a cause, and Newton's second law gives the quantitative relationship between force and change of motion. Newton's second law states that the net force acting upon an object is equal to the rate at which its momentum changes with time. If the mass of the object is constant, this law implies that the acceleration of an object is directly proportional to the net force acting on the object, is in the direction of the net force, and is inversely proportional to the mass of the object.[17]: 204?207 

A modern statement of Newton's second law is a vector equation:


where 𝑝 is the momentum of the system, and 𝐹 is the net (vector sum) force.[17]: 399  If a body is in equilibrium, there is zero net force by definition (balanced forces may be present nevertheless). In contrast, the second law states that if there is an unbalanced force acting on an object it will result in the object's momentum changing over time.[14]

In common engineering applications the mass in a system remains constant allowing as simple algebraic form for the second law. By the definition of momentum,

where m is the mass and v is the velocity.[4]: 9-1,9-2  If Newton's second law is applied to a system of constant mass, m may be moved outside the derivative operator. The equation then becomes


By substituting the definition of acceleration, the algebraic version of Newton's second law is derived:

[alancalverd]

I think you need to first understand what the meaning of a concept as it's currently understood by most of its users.

Not on a science forum. There are formal and precise definitions of important words like torque, power, energy, velocity, speed, exponential....which are not currently understood by most of the people who (mis)use the words.

I think the correspondents in this forum are well acquainted with Newton's laws, even if the people who feature in some videos aren't.

[Bored chemist]

I think the correspondents in this forum are well acquainted with Newton's laws,

I'm less sure about that.

Have you got to grips with the conservation of angular momentum yet?
https://www.thenakedscientists.com/forum/index.php?topic=80717.0

[hamdani yusuf (OP)]

Not on a science forum. There are formal and precise definitions of important words like torque, power, energy, velocity, speed, exponential....which are not currently understood by most of the people who (mis)use the words.

I was referring to people who use the concepts in practice.

[alancalverd]

Every garage mechanic knows what torque is.

[hamdani yusuf (OP)]

Every garage mechanic knows what torque is.

Most of us know that torque is rotational force. It's a force that can make stationary objects to rotate, or change their rotational speed. It's not just a force.

[Bored chemist]

Every garage mechanic knows what torque is.

Yes.
They realise that you need a torque to change the rotation of something (unless the moment of inertia changes).
Somthing like... Ok... let's say... the earth

[alancalverd]

It's not just a force.

which is why the unit is force x distance, as clearly written on your torque wrench.

[hamdani yusuf (OP)]

It's not just a force.

which is why the unit is force x distance, as clearly written on your torque wrench.

The torque wrench is mostly used for tightening bolts, where bolt tightness determines the performance of the machinery, hence must be controlled. If it's too loose, there is risk of the bolt being detached from the machinery due to vibration or thermal expansion and contraction. On the other hand, when it's too tight, there is risk of breaking the bolt itself, the thread, or gaskets.
We usually only care about the maximum torque applied through the torque wrench. How long the torque is applied, how far it causes the bolt to rotate, and how much energy is used to apply the torque to reach its set point is not much of a concern. These may cause our understanding on the concept of torque incomplete.

The law of conservation of energy can also be used to understand torque. If a force is allowed to act through a distance, it is doing mechanical work. Similarly, if torque is allowed to act through an angular displacement, it is doing work. Mathematically, for rotation about a fixed axis through the center of mass, the work W can be expressed as

The equation clearly implies that SI unit of torque is Joule per radian.
When unit of torque is stated as Newton meter, it's important to note that the meter here is for perpendicular distance with the direction of force.
But when Newton meter is used to express work, the meter here is for parallel distance with the direction of force.

If a quantity is expressed in Newton meter, more information is needed to determine whether it's a quantity of work or torque, because the distance in meter doesn't tell if it's parallel or perpendicular with the force in Newton (tangential or radial to the circular trajectory, respectively).
On the other hand, the unit Joule already tells that it's a dot product of Newton and meter, which means the distance in meter here is always parallel to the force in Newton. Expression of torque requires the conversion from parallel to perpendicular distance, which can be done by dividing it by angle of rotation.
IMO, expression of torque as Joule/radian is better for eliminating ambiguity. It's just an unfortunate path of history which lead us to this confusion, that the concept of energy wasn't explicitly quantified in a standard unit when the concept of torque was introduced.

 

[hamdani yusuf (OP)]

Here's an example to distinguish between torque and force.

A hammer-like metal object consists of a cube sandwiched between a pair of half cylinders. It's equipped with a handle with negligible mass. A force is applied to the end of the handle.

When the floor is frictionless, the force will only make the hammer slide horizontally, which means the net torque is zero.
But when the floor has high friction, the hammer can tumble, which means that the hammer has been rotated.

[Bored chemist]

These may cause our understanding on the concept of torque incomplete.

Unless you ask someone who talks about car engines.
https://spicerparts.com/calculators/horsepower-torque-calculator
The units there are particularly scrambled.
But it shows that they don't just use torque for bolts.

[hamdani yusuf (OP)]

These may cause our understanding on the concept of torque incomplete.

Unless you ask someone who talks about car engines.
https://spicerparts.com/calculators/horsepower-torque-calculator
The units there are particularly scrambled.
But it shows that they don't just use torque for bolts.

My comment that you quoted is about common torque wrench, which isn't often used to measure the torque of running engines.

[alancalverd]

We usually only care about the maximum torque applied through the torque wrench. How long the torque is applied, how far it causes the bolt to rotate, and how much energy is used to apply the torque to reach its set point is not much of a concern.

Consider a "physicist's bolt", perfectly elastic and with infinitesimal pitch and friction. It doesn't matter how many turns it takes to bring the bolt face into contact with the (perfectly elastic) flange since no work is done, but once in contact, any further rotation is compressing the flange and extending the bolt, so the final torque equals the potential energy stored in the bolt and flange.

A near-real-life approximation is a flange with an O-ring. The ring is much more compressible than the flange or the bolt, but the compression force is much greater than the frictional forces if you are using a new bolt, a decent washer, and the lubrication specified in the worksheet.. Now it is obvious that the tightening  torque at any point equals the elastic energy in the ring. 

In real real life, of course, the workshop only has old bolts, no graphite, and the store is closed. That's the difference between theoretical and experimental physics. And in engineering, the customer is screaming for completion by yesterday.

[hamdani yusuf (OP)]

Now it is obvious that the tightening  torque at any point equals the elastic energy in the ring. 

What is the ratio between them?

[alancalverd]

1:1, thanks to the  principle of conservation of energy.

[hamdani yusuf (OP)]

1:1, thanks to the  principle of conservation of energy.

How does it explain this equation?

[hamdani yusuf (OP)]

1:1, thanks to the  principle of conservation of energy.

The 1:1 ratio only applies if the angle of rotation is 1 radian, which makes the arc length equals the radius. Different amount of rotational angle gives different ratio.

[hamdani yusuf (OP)]

I asked Gemini.
Why Radians are Dimensionless?

A radian is a measure of an angle, defined as the ratio of the arc length of a circle to its radius.
Since both the arc length and the radius are measured in units of length (like meters or centimeters), these units cancel out when calculating the radian.
Therefore, a radian is essentially a ratio of two lengths, resulting in a dimensionless quantity.
This is unlike other units like meters, seconds, or kilograms, which have specific dimensions (length, time, and mass, respectively).
In essence, a radian is a pure number that represents an angle, without any associated physical dimension.

I continued.
Why Amount of Substance Has a Dimension?

The amount of substance, measured in moles, does indeed have a dimension. It's one of the seven base units in the International System of Units (SI).
Why?
 * Distinct from Counting: While it might seem like simply counting particles, the mole is a macroscopic unit used to quantify microscopic entities (atoms, molecules, ions, etc.). It's analogous to using "dozen" to count eggs rather than individually counting each egg.
 * Relating to Other Quantities: The mole is essential for connecting microscopic properties (like atomic mass) to macroscopic properties (like mass). For example, the ideal gas law (PV = nRT) uses the amount of substance (n) to relate pressure, volume, temperature, and the gas constant.
 * Consistency in Calculations: Assigning a dimension to the amount of substance ensures dimensional consistency in equations. It helps prevent errors in calculations and ensures that the units on both sides of an equation match.
Key Points:
 * The mole is a base unit, independent of other base units like mass, length, or time.
 * It's a measure of the quantity of a substance, not its mass or volume.
 * Avogadro's number (approximately 6.022 x 10^23) defines the number of particles in one mole.
By recognizing the amount of substance as a distinct dimension, we can accurately quantify and manipulate matter at both the microscopic and macroscopic levels.

Essentially, the angle of rotation can be thought as the amount of waves. If an object is rotated by 6π radians, it undergoes 3 waves.

On the other hand, the amount of substance can be thought as ratio between the mass of the whole substance and the mass of single individual substance.

If consistency has any significance in setting up a standard, the angle of rotation should also have a dimension assigned, instead of being dimensionless, which has led to a widespread confusion.