[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.

Here's a linear analogy for the situation.
A 10 Newton weight is put on a table. It continuously apply 10 N force to the table. But it stays on the table instead of falling down, because there is normal force by the table to the weight, resulting in zero net force.

[alancalverd]

When someone says that the applied torque is 3.18 Nm, what they really mean is 3.18 Nm/rad.

No they don't. The applied torque of a 3.18 N weight hanging from a 1 m lever is 3.18 Nm by definition. If you double the weight and nothing moves, what happened to the rad? 

[hamdani yusuf (OP)]

When someone says that the applied torque is 3.18 Nm, what they really mean is 3.18 Nm/rad.

No they don't. The applied torque of a 3.18 N weight hanging from a 1 m lever is 3.18 Nm by definition. If you double the weight and nothing moves, what happened to the rad? 

What's the net torque? Is it non-zero?
Your definition is not complete. It's only true if the direction of the force is perpendicular to the lever. Also, the position of the fulcrum or pivot point isn't changed by the force.

[hamdani yusuf (OP)]

Here's a linear analogy for the situation.
A 10 Newton weight is put on a table. It continuously apply 10 N force to the table. But it stays on the table instead of falling down, because there is normal force by the table to the weight, resulting in zero net force.

F = m.a
If you don't take the normal force into account, you will wonder where the acceleration of the stationary weight is.

[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.

Work done by a torque is the torque multiplied by rotational angle.
W = τ. θ
So, at least one of the unit of work or torque contains unit of angle in it.
Work can be done in linear motion. On the other hand, torque is specifically used in rotational motion. By these constraints, the unit of angle must appear somewhere in the denominator of torque unit.

[alancalverd]

Imagine a weightless tube, 2 m long, with a frictionless pivot in the middle and a 0.5 kg rocket nozzle at each end - an ideal firework, but powered by compressed air fed from the center. Turn on the  air supply so each nozzle delivers 0.5N of thrust. The total torque is either 1 Nm or 1 Nm/rad.

Describe the subsequent motion of the system using both definitions of torque.

[hamdani yusuf (OP)]

Imagine a weightless tube, 2 m long, with a frictionless pivot in the middle and a 0.5 kg rocket nozzle at each end - an ideal firework, but powered by compressed air fed from the center. Turn on the  air supply so each nozzle delivers 0.5N of thrust. The total torque is either 1 Nm or 1 Nm/rad.

Describe the subsequent motion of the system using both definitions of torque.

The kinetic energy after the torque is applied for 1 radian is 1 Nm = 1 J.
The velocity is square root of (2*energy/mass) = sqrt(4) = 2 m/s
I assumed friction is negligible. Thus no energy is lost to the environment. All the work done is converted to kinetic energy.
What would happen to the system if the torque is 1 Nm? (without specifying the rotational angle)

[Bored chemist]

Did you all know that the SI unit of pressure is joules per cubic metre?

So, by analogy with Alan's point...

No they don't. The applied torque of a 3.18 N weight hanging from a 1 m lever is 3.18 Nm by definition. If you double the weight and nothing moves, what happened to the rad? 

The applied pressure of a 3.18 N weight on a square metre of area  is 3.18 J/m^3 by definition. If you double the weight and nothing moves, what happened to the m^3?

Units are just weird that way.

[hamdani yusuf (OP)]

When someone says that the applied torque is 3.18 Nm, what they really mean is 3.18 Nm/rad.

No they don't. The applied torque of a 3.18 N weight hanging from a 1 m lever is 3.18 Nm by definition. If you double the weight and nothing moves, what happened to the rad? 

What's the net torque? Is it non-zero?
Your definition is not complete. It's only true if the direction of the force is perpendicular to the lever. Also, the position of the fulcrum or pivot point isn't changed by the force.

Since you cannot answer my questions, I'll help you out.
The net torque is zero.

[alancalverd]

Then why am I leaning on the torque wrench, and why doesn't it fly backwards when I release it?

What would happen to the system if the torque is 1 Nm?

It would continue to accelerate at a constant dω/dt.

[hamdani yusuf (OP)]

The Lever Paradox

When I was making this double decker newton's cradle I released something very strange about levers.

Oddly, the distance that seems to work well for long lever matches root 12 which matches the moment of inertia of a spinning rod *spinning from its end*. So it's as if we're matching the moment of inertia of just one side of the rod. That doesn't sit right with me though. Hmmm.

This video shows how basic equation for torque in lever isn't adequate to describe dynamic systems.

[hamdani yusuf (OP)]

Then why am I leaning on the torque wrench, and why doesn't it fly backwards when I release it?

I believe you understand how friction work, either static or kinetic type, especially in a system of linear motion. Here's the explanation by Gemini.

Static and kinetic friction are two types of friction that act on objects in contact. The key difference between them lies in the state of motion of the objects:
Static Friction:
 * Acts on objects at rest: Static friction is the force that prevents two surfaces from sliding against each other when they are stationary relative to each other.
 * Variable force: It can vary in magnitude, increasing or decreasing depending on the force trying to initiate movement.
 * Has a maximum value:  Static friction has a limit. Once the applied force exceeds this limit, the object will start to move.
Kinetic Friction:
 * Acts on objects in motion: Kinetic friction is the force that opposes the motion of two surfaces sliding against each other.
 * Constant force: Unlike static friction, kinetic friction is generally constant regardless of the speed of the objects.
 * Lower than static friction: The force of kinetic friction is usually less than the maximum force of static friction. This means it takes more force to start an object moving than to keep it moving.
Everyday Examples:
 * Static friction: Prevents a book from sliding off a tilted surface, keeps your shoes from slipping on the floor when you walk.
 * Kinetic friction: Slows down a sled sliding down a hill, allows you to apply the brakes on a bicycle.
Mathematical Representation:
Both static and kinetic friction forces are calculated using the following formulas:
 * Static Friction (Fs): Fs ≤ μs * N, where μs is the coefficient of static friction and N is the normal force between the surfaces.
 * Kinetic Friction (Fk): Fk = μk * N, where μk is the coefficient of kinetic friction and N is the normal force between the surfaces.
Key takeaway:
Static friction keeps things from moving initially, while kinetic friction opposes the motion of things already moving.

[alancalverd]

Stating the bloody obvious is not an explanation! That would require a statement of why sliding friction is less  than static friction.

[hamdani yusuf (OP)]

Stating the bloody obvious is not an explanation! That would require a statement of why sliding friction is less  than static friction.

I thought you already knew that.

static versus dynamic friction

Friction coefficient, how to demonstrate the difference between static and dynamic friction in a physics experiment?

Gemini's answer to your question.

That's a great question! It seems counterintuitive that it's easier to keep something moving than it is to start it moving. Here's the breakdown of why sliding friction (kinetic friction) is less than static friction:
1. The Nature of Surfaces:
 * Microscopic Interactions: Even surfaces that appear smooth to the naked eye have microscopic bumps and ridges.
 * Interlocking: When two objects are at rest, these irregularities have time to settle into each other, creating strong "interlocking" points. This interlocking is what static friction needs to overcome to initiate movement.
2. Time Factor:
 * At Rest: When objects are at rest, the surfaces have time to conform and maximize their contact area, leading to more points of interlocking.
 * In Motion: When an object is already sliding, the irregularities don't have as much time to settle into each other. The "interlocking" is less pronounced. Imagine trying to quickly weave your fingers together versus doing it slowly and carefully ? the quick weave won't be as strong.
3. "Breaking" vs. "Maintaining"
 * Static Friction: Static friction is about "breaking" those initial interlocking points. It takes more force to overcome this initial resistance.
 * Kinetic Friction: Kinetic friction is about "maintaining" motion. Once the object is moving, you're essentially just continuously breaking and reforming weaker, temporary bonds. This requires less force.
In simpler terms:
Think of it like pushing a heavy box. It takes a lot of effort to get it moving from a standstill (static friction). But once you have it sliding, it's easier to keep it going (kinetic friction) because you're not constantly having to overcome that initial "sticking" force.
Key takeaway:
The stronger interlocking of surfaces at rest leads to a higher static friction, while the constantly changing and less pronounced interlocking during motion results in a lower kinetic friction.

Another analogy.
https://youtube.com/shorts/ec_ek3xQvNc?feature=shared

[Bored chemist]

You really need to stop using AI.

[hamdani yusuf (OP)]

You really need to stop using AI.

why?

How AI Will Answer Questions We Haven?t Thought to Ask | Aravind Srinivas | TED

Human potential will only accelerate with AI answering questions better and faster than ever before, says Aravind Srinivas, cofounder and CEO of conversational search engine Perplexity. He examines the trends driving new AI-powered tools that nourish curiosity and creativity ? and how they might usher in a new era of intellectual growth and discovery. "Knowledge does not really care about who you are, where you're from or who you have access to. Rather, what matters is the next question you're going to ask," says Srinivas. (Recorded at TEDAI San Francisco on October 22, 2024)


00:07 - AI innovation sees a rise in academic involvement among tech founders.
01:43 - Larry Page predicted AI would revolutionize search capabilities.
03:04 - AI will enhance human understanding and questioning.
04:32 - AI enhances human curiosity by generating questions beyond our current understanding.
06:00 - AI empowers users to ask questions confidently and receive trustworthy answers.
07:19 - AI democratizes access to knowledge and answers for everyone.
08:50 - AI democratizes knowledge, igniting endless curiosity and question-asking potential.
10:11 - AI enhances human curiosity by guiding us to new questions.

[Bored chemist]

You really need to stop using AI.

why?

Two reasons.
The first is that there's no guarantee that they don't talk nonsense.
The second is neatly illustrated by the video you posted. The AI seems to have largely missed that factor.

[hamdani yusuf (OP)]

You really need to stop using AI.

why?

Two reasons.
The first is that there's no guarantee that they don't talk nonsense.
The second is neatly illustrated by the video you posted. The AI seems to have largely missed that factor.

Is there any guarantee that humans don't talk nonsense?

Which factor?

[hamdani yusuf (OP)]

https://chng.it/dXwF228mj4

I've started a petition to Standardize the Unit of Torque as Joule per Radian (J/rad) Instead of Newton-Meter (N.m).

The Issue
Petition Summary:
We call upon the International System of Units (SI) and global scientific bodies to standardize Joule per Radian (J/rad) as the official unit for torque, replacing the ambiguous Newton-meter (N?m). This change will eliminate confusion between torque and work/energy, improving clarity in physics, engineering, and education.

Why This Matters:

1. Ambiguity in SI Units ? Currently, both torque and work/energy are expressed in N?m, despite being fundamentally different quantities. Torque is a vector (rotational force), while work is a scalar (energy transfer). This leads to misinterpretations in academic and industrial contexts.


2. Clarity in Scientific Communication ? Using Joule per Radian (J/rad) aligns torque directly with its definition: energy per unit angular displacement. This mirrors the linear counterpart (work = force ? displacement), making equations more intuitive.


3. International Consistency ? Many fields, such as mechanical engineering and physics, already use J/rad in practical calculations. Formal adoption would unify scientific literature and teaching materials.

 

Proposed Change:

Officially define torque in Joules per Radian (J/rad) within the SI system.

Encourage textbooks, research papers, and engineering standards to transition to the new unit.


Join Us!
Sign this petition to support a clearer, more logical unit system. Let?s urge ISO, NIST, BIPM, and other standardization bodies to take action!

[alancalverd]

Human potential will only accelerate with AI answering questions better and faster

....or as approved by the Government of China, the Diktator of America, the Pope, or whatever nonsense is currently fashionable in cyberspace, depending on who last programmed it and how.

Beware of Arselicking Ignorance - you don't know where its tongue has been.