[hamdani yusuf (OP)]

Specifying torsional stiffness as Nm/rad squared will produce multiple errors in any subsequent application. It is a linear function of rotation, not a quadratic. I have to come to the unfortunate conclusion that Hamdani is either unwilling or incapable of learning.

Name one.

[hamdani yusuf (OP)]

For those who doesn't know it yet,
the time derivative of angular momentum is called torque.

So when you rotate an object at constant angular velocity against friction, the applied torque is zero.

Great! Free heat!

By simply inventing an absurd definition of a term that everyone else understands, you have solved the world's energy problems and destroyed the economies of several evil dictatorships!

When a rotating object is decelerated by friction, there is reduced angular momentum, which means there's a negative torque. If you put some work to cancel out the deceleration, the net torque will be zero.
Your repeated confusion comes from your failure to identify the net torque.

[alancalverd]

Name one.

A taut-band voltmeter would not have a linear scale. They do.
Cavendish's measurement of G  would not correspond with later estimates. It does.

I could go on. I won't,

[hamdani yusuf (OP)]

3. To increase the potential energy of an object. Like lifting things against gravitational field. Compressing a spring or other elastic objects.

In contrast, the first category described change in kinetic energy of an object.

Some systems might involve a combination of 3 categories above. For example, pumping water uphill involves increasing kinetic and potential energy of the water, while also working against friction.

[hamdani yusuf (OP)]

Name one.

A taut-band voltmeter would not have a linear scale. They do.

They either do or don't. They can't be both.

[alancalverd]

My point precisely. Taut-band meters are linear. If torsional stiffness were a function of 1/θ², they wouldn't be linear.

If you want to deny the obvious, you might find a more receptive audience in  a philosophical, religious or political forum, and if you want to promulgate confusion, you could try talking to educationalists (not teachers) whose job is to convey their own incomprehension to children.

[paul cotter]

Thank you ,Alan, you saved me the bother of further futile argumentation with Hamdani. I don't know why I get involved in these pointless useless discourses, having dropped out previously due to utter exasperation- I think more would be achieved by bashing one's head against a concrete wall.

[hamdani yusuf (OP)]

My point precisely. Taut-band meters are linear. If torsional stiffness were a function of 1/θ², they wouldn't be linear.

If you want to deny the obvious, you might find a more receptive audience in  a philosophical, religious or political forum, and if you want to promulgate confusion, you could try talking to educationalists (not teachers) whose job is to convey their own incomprehension to children.

I've addressed your objection previously. You just need to read it in order to understand it.

Torsional stiffness is a linear function of rotation and you have it as quadratic. That is a major fail that you cannot square.

You can also find squared unit of distance in the unit for work, even though it is linear with the displacement. It renders your objection invalid.

[alancalverd]

I'm quite happy dealing with people who don't know much physics, but not with someone who refuses to learn.

[hamdani yusuf (OP)]

I'm quite happy dealing with people who don't know much physics, but not with someone who refuses to learn.

Between these two tables, which one is more consistent?

You don't seem to be aware of the inconsistency in current standard units of rotational quantities, as shown clearly in this table.


Compare them with the new proposed standard units, which are consistent with the relating equations.

[alancalverd]

Your unit of moment of inertia is meaningless and not related to its definition.

To misquote Einstein, the symptom of insanity is repeating the same mistake in the hope of convincing yourself that you were right.

[hamdani yusuf (OP)]

Your unit of moment of inertia is meaningless and not related to its definition.

To misquote Einstein, the symptom of insanity is repeating the same mistake in the hope of convincing yourself that you were right.

What is your definition of rotational inertia?

In the second table, you can see that the unit of lkinetic energy is identical for linear motion and rotational motion.
In linear motion, Ek =  1/2 m.v^2
In rotational motion, Ek = 1/2 I.ω^2
From these equations, you should be able to deduce that the proper unit for rotational inertia is identical to the unit for energy divided by angular velocity squared.

Power is the time derivative of energy. If you use it to derive the unit of rotational inertia, you should get the same result.

If you still struggle to follow my reasoning, please let me know which part needs further elaboration.

If you know someone else who has more knowledge of fundamental physics, you can ask them to analyze my results.

[hamdani yusuf (OP)]

I'm quite happy dealing with people who don't know much physics, but not with someone who refuses to learn.

https://blog.learnlife.com/learn-unlearn-relearn
?The illiterate of the future are not those who can?t read or write but those who cannot learn, unlearn, and relearn.? Alvin Toffler

Learning something, if you?re actually interested in it, is pretty much always something enjoyable. Learning some things takes longer than others (though not to confuse learning with mastery, which can take a lifetime), but we do learn something every day.

Unlearning, however, is something quite different. You might be forgiven for thinking it means knowledge just disappearing from your memory, like the way your University degree in German is reduced to you frantically gesturing at a sandwich in Hamburg just 10 years later and hoping they understand that you want to buy it.

It?s not that. Unlearning is challenging and deconstructing things that are embedded in your way of thinking, acting and reacting. There are a lot of metaphors for unlearning. Chipping away at the old paint before you put on a fresh coat. Clearing away the vegetation before planting something new.

They all point to the same thing; the previous ideas, beliefs, assumptions, etc, must be completely removed for the new one to flourish. They cannot overlap, just as one must eradicate all of the old roots before planting new flowers.

Teachers go through an unlearning process when they enter a new learning environment outside the mainstream model. Chris Dede, of the Harvard Graduate School of Education tells us that:

?transformative change is very challenging because participants not only must learn new skills, but also must ?unlearn? almost unconscious beliefs, assumptions, practices, and values about the nature of [...] learning?

There are things that we have just accepted as ?fact?, and they have simply become part of the furniture. The teacher delivers the knowledge, and the learners ?study? or ?listen?. Tests equate to competence and everyone can be measured on the same scale, so that the grade tells you how good you are. You know what? The fun part comes when you decide that maybe that old chair just doesn?t fit any more.

[hamdani yusuf (OP)]

Thank you ,Alan, you saved me the bother of further futile argumentation with Hamdani. I don't know why I get involved in these pointless useless discourses, having dropped out previously due to utter exasperation- I think more would be achieved by bashing one's head against a concrete wall.

If you can't come up with your own explanation, then your best option is to select one of someone else's explanations that you think is the most reasonable. But to select reasonably, you need to identify the reason why you prefer that explanation over the others. Some of possible reasons are:
Simplicity
Usefulness
Generality
Consistency
Familiarity
Publicity
Popularity
Authority

[hamdani yusuf (OP)]

Your unit of moment of inertia is meaningless and not related to its definition.

To misquote Einstein, the symptom of insanity is repeating the same mistake in the hope of convincing yourself that you were right.

What is your definition of rotational inertia?

In the second table, you can see that the unit of lkinetic energy is identical for linear motion and rotational motion.
In linear motion, Ek =  1/2 m.v^2
In rotational motion, Ek = 1/2 I.ω^2
From these equations, you should be able to deduce that the proper unit for rotational inertia is identical to the unit for energy divided by angular velocity squared.

Power is the time derivative of energy. If you use it to derive the unit of rotational inertia, you should get the same result.

If you still struggle to follow my reasoning, please let me know which part needs further elaboration.

If you know someone else who has more knowledge of fundamental physics, you can ask them to analyze my results.

The definition of a physical concept doesn't occur in isolation. It depends on its relationship with other concepts which are more fundamental or more familiar with us.
In the case of rotational quantities described in this thread, they are defined as rotational analogies of linear quantities that we are more familiar with because of their more simplicity and being more well developed earlier.

[alancalverd]

What is your definition of rotational inertia?

The quantity you call rotational inertia is more commonly and in my opinion more logically called moment of inertia,
I =  ∑mr²,
where r is the distance of each element of mass from whatever point we define as the center of interest. There is no mention of angle.

Your confusion probably arises from the use of the word "rotational". I is obviously important if we want to rotate an object, and that would define r in terms of our chosen axis  of rotation. Consider a dumbbell: two point masses of m = 1 separated by  a massless rod  of length 2. If we measure r from the geometric center, to twirl the majorette's baton, obviously I  = 2. If we measure from one end, to use it as a weapon, I = 4. No mention of any angle.

In the case of rotational quantities described in this thread, they are defined as rotational analogies of linear quantities

I am sure that you would be one of the first to warn the naive about false or misleading analogies. Beware of falling into a trap of your own making!

[paul cotter]

Torsional stiffness is linear in the variable of rotation. No amount of extraneous digressions can save your concept as it has been proven to be an epic fail.

[hamdani yusuf (OP)]

What is your definition of rotational inertia?

The quantity you call rotational inertia is more commonly and in my opinion more logically called moment of inertia,
I =  ∑mr²,
where r is the distance of each element of mass from whatever point we define as the center of interest. There is no mention of angle.

Your confusion probably arises from the use of the word "rotational". I is obviously important if we want to rotate an object, and that would define r in terms of our chosen axis  of rotation. Consider a dumbbell: two point masses of m = 1 separated by  a massless rod  of length 2. If we measure r from the geometric center, to twirl the majorette's baton, obviously I  = 2. If we measure from one end, to use it as a weapon, I = 4. No mention of any angle.

In the case of rotational quantities described in this thread, they are defined as rotational analogies of linear quantities

I am sure that you would be one of the first to warn the naive about false or misleading analogies. Beware of falling into a trap of your own making!

Why is it called moment ?

The rotational angle is there as the ratio between rotational displacement and rotational radius.

[hamdani yusuf (OP)]

Torsional stiffness is linear in the variable of rotation. No amount of extraneous digressions can save your concept as it has been proven to be an epic fail.

The force is proportional to the rotational angle. But the energy is proportional to the rotational angle squared.

[hamdani yusuf (OP)]

A ball is spinning at 1 rotation per second. If its rotational kinetic energy is 1 Joule, what's the rotational inertia of the ball?

What's the angular momentum?