[hamdani yusuf (OP)]

2π rad/s = 1 cycle/second = 1 Hz = 1/s

Only in the specific case of continuous circular motion, which you have not stated. A standard instrument turn in an airplane is π rad/minute, but you couldn't call it 0.052 Hz unless you are in a spin or spiral dive, which is not a happy place to be.

English spelling is broken.

Inappropriate use of "broken". English spelling is interesting because the words have many historical sources and there is no official body to limit the vocabulary, which makes it a very robust and flexible language, but it's no more of a "nightmare" than Chinese. You just have to learn the words individually. If you want to use a language whose spelling and pronunciation are always logical and consistent, you can use German. But for some reason, more folk prefer English.

What belief or idea are you willing to question this week?

Any and every belief that is not supported by observation.

Consistency doesn't seem to be the human's particular strength.

Consistency can be weakness. Evolution and adaptability work better in a dynamic world. Otherwise we'd be stuck with Genesis, phlogiston, and an ultraviolet catastrophe. Farseebox (all Saxon roots, consistent pronunciation, like Fernsehapparat) or television (Latin/Greek bastard word that everyone uses)? Mind you, my favorite word of all time was written on the HT rectifier of an old German valve television: "Fernsehapparathochspannunggleichricter" - absolutely logical!

So, in some cases, 1 rad equals 1. But in some other cases, 1 rad equals 1/(2π). You depend on unstated context to tell which is which.

Standards are developed specifically for consistency. For practical uses, there are rules, like rule of thumb. They are shortcuts which are good enough for most applications, so they are efficient, but lack of generality.

[alancalverd]

So, in some cases, 1 rad equals 1. But in some other cases, 1 rad equals 1/(2π). You depend on unstated context to tell which is which.

Nonsense. 1 radian is always the angle that is subtended by 1/2π of a circle. Like a degree, which is subtended by 1/360 of a circle. The context is irrelevant.

[hamdani yusuf (OP)]

So, in some cases, 1 rad equals 1. But in some other cases, 1 rad equals 1/(2π). You depend on unstated context to tell which is which.

Nonsense. 1 rad is always the angle that is subtended by 1/2π of a circle. Like a degree, which is subtended by 1/360 of a circle. The context is irrelevant.

Those nonsense are just the implications of following current SI standard. One of your options is simply to ignore them and move on. Another option is to revise current SI standard so that it doesn't lead to contradiction.
If you read the appendix of SI document referred in my previous post, you can find that it has been revised many times, including the treatment of radian. So, revising it one more time is not strictly forbidden.

[alancalverd]

You have not shown any "contradiction", nor any reason to redefine the radian or invent a new unit with dimensions newton meter per radian (which would immediately confuse it with torsional stiffness).

If you want to define some other quantity, by all means do so, but please don't delude yourself into thinking that anyone (other than Boeing accountants and you)  doesn't understand the meaning and use of torque.

A word of advice:  when talking to professionals, don't use words like "equals" loosely - they won't take you seriously if you misuse their language.

[paul cotter]

When in a hole the perceived wisdom is to stop digging. I suggest that you, Hamdani, should stop this nonsense now as you are making a fool of yourself. That statement by Alan, in which he gives the definition of the radian is absolutely correct and is an unassailable statement. Give it up.

[alancalverd]

A unit that we often use in mapping, radiation protection, and photometry, is the steradian. I wonder what Hamdani thinks of its dimensionality?

And be cautious when using rad as an abbreviation - it is also a US and Russian unit of ionising radiation dose, though it is no longer current in civilised countries. So you might calculate the radiation dose from a point nuclear incident to, say, livestock or standing crops, in terms of rad per rad!

[paul cotter]

I get confused by radiologic metrics, rems, rads, Sieverts, Curies . I suppose that if I had application for these I would remember their interrelations.

[alancalverd]

The interrelations involve lots of dimensionless numbers and best guesses (politely known as expert consensus values) - Hamdani would have a fit!

Kinetic energy is released to matter ("kerma" - measured in joules per kilogram) by ionising radiation, but some of that energy is scattered out of the primary target, so what remains is called absorbed dose (measured in grays, also J/kg).

But different forms of radiation have different relative biological  effectiveness in vitro so we define equivalent dose as absorbed dose x RBE (calculated in sieverts, but still J/kg x a dimensionless consensus value between 1 and 20).

But various organs have different radiosensitivities and functional significance in vivo so the statutory basis of radiation protection is effective dose, the sum of all the equivalent doses delivered to a body multiplied by the tissue   weighting factors (consensus values which add up to 1 for the whole body), also expressed in sieverts.

So far, so SI. But there is a significant hangover from earlier cgs units in intellectual backwaters and banana republics (USA and Russia), where the analog of kerma is the rontgen, absorbed dose is measured in rads, and effective dose is reported in rem ("rontgen equivalent man").

The curie is a historic (though current in the USA) measure of the activity of a radionuclide source, equal to the number of disintegrations of a gram of Ra226 per second (3.7 x 10¹⁰). In civilised countries it has been replaced by the becquerel, a reciprocal second but not to be confused with the hertz, which is reserved for strictly cyclic phenomena whereas the Bq is a time average of essentially random events.   

The good news, as far as I am concerned (I mostly work with medical x-rays) is that the gray/sievert consensus conversion factor is set at 1 for 200 kV x-rays uniformly irradiating a human. The "good" news (inverted commas very significant) is that we now have hard evidence that the LD50/30 is almost exactly 5 Sv, so benefit/risk assessments have a sound empirical basis.

The bad news, in my opinion, is that we don't have credible experimental values for α radiation, just a consensus figure of 20. If this was increased to around 100 - 200, at least for plutonium, a lot of anomalous epidemiology would be resolved.

[hamdani yusuf (OP)]

You have not shown any "contradiction", nor any reason to redefine the radian or invent a new unit with dimensions newton meter per radian (which would immediately confuse it with torsional stiffness).

If you want to define some other quantity, by all means do so, but please don't delude yourself into thinking that anyone (other than Boeing accountants and you)  doesn't understand the meaning and use of torque.

A word of advice:  when talking to professionals, don't use words like "equals" loosely - they won't take you seriously if you misuse their language.

Do you know that there is an equation W = τ.θ?
Do you know that there is an equation P = τ.ω?
Do you think that 1 Newton meter equals to 1 Joule?
What do you think 1 Joule/radian equals to?

[hamdani yusuf (OP)]

When in a hole the perceived wisdom is to stop digging. I suggest that you, Hamdani, should stop this nonsense now as you are making a fool of yourself. That statement by Alan, in which he gives the definition of the radian is absolutely correct and is an unassailable statement. Give it up.

You need to read more carefully. I don't propose to change the definition of radian. My previous post was meant to show that current practice contradicts the definition of radian.
The change that I proposed in my petition is  for the unit of rotational radius to be distinguished from geometric radius, according to the equations like
v = ω . r
s = θ . r
Which require rotational radius to be expressed in meter per radian.
If this requirement is adhered consistently, applying all definitions and equations of rotational motion produces coherent and consistent units as shown in my tables.

It's not to change the definition of radian or any other units.

[hamdani yusuf (OP)]

A unit that we often use in mapping, radiation protection, and photometry, is the steradian. I wonder what Hamdani thinks of its dimensionality?

And be cautious when using rad as an abbreviation - it is also a US and Russian unit of ionising radiation dose, though it is no longer current in civilised countries. So you might calculate the radiation dose from a point nuclear incident to, say, livestock or standing crops, in terms of rad per rad!

I think the title of this thread has clearly provided the context for rotational motion.

[Bored chemist]

The irony of this term...
https://en.wikipedia.org/wiki/Spat_(angular_unit)

:-)

[Bored chemist]

A unit that we often use in mapping, radiation protection, and photometry, is the steradian. I wonder what Hamdani thinks of its dimensionality?

And be cautious when using rad as an abbreviation - it is also a US and Russian unit of ionising radiation dose, though it is no longer current in civilised countries. So you might calculate the radiation dose from a point nuclear incident to, say, livestock or standing crops, in terms of rad per rad!

You should get that added to the list of "cursed units".

[alancalverd]

Do you think that 1 Newton meter equals to 1 Joule?

Unqualified and ignorant use of "equals". A force of 1 N moving through 1m in the line of action of that force does 1 J of work, but a static force of 1N applied normal to a radius of 1 m from a pivot is  not doing any work.

What do you think 1 Joule/radian equals to?

Nothing in particular. It could be the energy expended by a flat beam  of pulsed radiation (phased array radar, sonar...), or the work done against friction to turn a screw, or the torsional stiffness of a clock spring, or anything else you can think of where the unit is appropriate.

[alancalverd]

s = θ . r

only for the arc of a circle.

Radius of curvature is ds/dθ for any shape, and is not generally a constant. Depending on where you put your origin, r can be negative.

And 3D shapes can be even more interesting. But they can still be made to rotate. 

[alancalverd]

You should get that added to the list of "cursed units"

I do have a serious beef about SI units, particularly the multipliers.

M, m, μ (handwritten mu) are frequently misused or misread in clinical practice and only common sense prevents serious over- or under-dosing.

I've always  preferred to use the old "line printer exponent" E6, E-3, E-6, and mental estimation is a lot easier if you always use "scientific" notation with one significant figure before the decimal point and whatever exponent is then appropriate, e.g. 6.23E23.

And having saddled themselves with SI multipliers, x-ray manufacturers now go out of their way to display "dose area product" (a proxy for the radiation energy imparted to a patient through an entire examination) in pretty well any unit you can imagine: Gy.cm², uGy.m², cGy.dm²....you name it... then expect the operator to record the value and the employer to somehow normalise the doses across umpteen different machines without knowing what units the operator has written down.....

Time was that Solartron, a British manufacturer of oscilloscopes, offered to calibrate their equipment in any unit the customer wanted, including my favorite "millifurlongs per microfortnight". Perfect for discussion over a warm beer at a cricket match.

[paul cotter]

I know what you mean as I have been in error with my multipliers and had to be corrected(thank you, BC).

[hamdani yusuf (OP)]

Rotational Quantities 5: Derivation of Non-circular Motion
This video describes the derivation of quantities for non-circular motion, by introducing radial and orthogonal quantities.

I reuploaded the video after correcting some typos, in order to avoid unnecessary confusions.

[hamdani yusuf (OP)]

Do you think that 1 Newton meter equals to 1 Joule?

Unqualified and ignorant use of "equals". A force of 1 N moving through 1m in the line of action of that force does 1 J of work, but a static force of 1N applied normal to a radius of 1 m from a pivot is  not doing any work.

What do you think 1 Joule/radian equals to?

Nothing in particular. It could be the energy expended by a flat beam  of pulsed radiation (phased array radar, sonar...), or the work done against friction to turn a screw, or the torsional stiffness of a clock spring, or anything else you can think of where the unit is appropriate.

It can be the torque needed to keep a windlass with 1 meter radius to hold a bucket weighing 1 Newton from accelerating, i.e. the speed is constant.

[hamdani yusuf (OP)]

s = θ . r

only for the arc of a circle.

Radius of curvature is ds/dθ for any shape, and is not generally a constant. Depending on where you put your origin, r can be negative.

And 3D shapes can be even more interesting. But they can still be made to rotate. 

So, radius of curvature would also has meter per radian unit.