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QuoteIt shows that defining 1 radian as dimensionless number with value of 1 is problematic. Not at all. As the initial figure is 3600 revolutions per minute, the angular speed is (3600/60) x 2π = 377 rad/sec. If you want to know the appropriate strobe frequency for a single mark on a rotating cylinder, it's obviously 3600/60 = 60 Hz. Where's the problem? It happens that dividing a circle into 2π radians is more convenient for physics than any other measure of angle, but you could propose a "coherent" standard where a circle has a value of 1. Then the angular speed would be 60 c/sec, the strobe frequency would be 60 Hz, and, for instance, the angle we call π/4 would be 0.125c. So what?
It shows that defining 1 radian as dimensionless number with value of 1 is problematic.
Let's get back to the windlass. We have a weightless, frictionless rope around a 0.5 m diameter cylinder that can rotate on frictionless pivots. The moment of inertia of the cylinder is 1 kg.m2. We apply a brake, hang a 4 N bucket on the rope, then release the brake. Conventionally and by common sense the torque is a constant 1 N.m so the cylinder rotates with a constant angular acceleration of 1 rad/sec2. Very reasonable. But suppose the torque was 1 N.m/rad. The initial acceleration would be 1 sec-1, which is, frankly, meaningless, and after one turn (2π rad) the torque would have increased!
1 Radian in SI is defined as a dimensionless number with value of 1
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius.[2] The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit,[2] defined in the SI as 1 rad = 1[3] and expressed in terms of the SI base unit metre (m) as rad = m/m.[4] Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.
You are confused because you are mixing SI unit for angular inertia with the equationally consistent unit for angular force.
Post #1181 by Alan is entirely consistent and if you cannot see that you are more confused than I had previously thought. Or maybe you are being deliberately obstinate because you have been soundly proved to be in error and you can't accept reality.
Quote1 Radian in SI is defined as a dimensionless number with value of 1No. QuoteThe radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. It is defined such that one radian is the angle subtended at the centre of a circle by an arc that is equal in length to the radius.[2] The unit was formerly an SI supplementary unit and is currently a dimensionless SI derived unit,[2] defined in the SI as 1 rad = 1[3] and expressed in terms of the SI base unit metre (m) as rad = m/m.[4] Angles without explicitly specified units are generally assumed to be measured in radians, especially in mathematical writing.If you stick to the facts, you won't be confused by your own fantasies!
QuoteYou are confused because you are mixing SI unit for angular inertia with the equationally consistent unit for angular force.Me confused? Surely α = τ/I. All I have done is substitute your proposed unit of τ.
Quote from: alancalverd on 16/06/2025 11:55:27Let's get back to the windlass. We have a weightless, frictionless rope around a 0.5 m diameter cylinder that can rotate on frictionless pivots. The moment of inertia of the cylinder is 1 kg.m2. We apply a brake, hang a 4 N bucket on the rope, then release the brake. Conventionally and by common sense the torque is a constant 1 N.m so the cylinder rotates with a constant angular acceleration of 1 rad/sec2. Very reasonable. But suppose the torque was 1 N.m/rad. The initial acceleration would be 1 sec-1, which is, frankly, meaningless, and after one turn (2π rad) the torque would have increased! You are confused because you are mixing SI unit for angular inertia with the equationally consistent unit for angular force.
How do you fix this?
Oh dear. You have equated force and torque. What do you mean by "radial" units? Everyone else uses watts for power.Whish is why we don't like using W to signify anything elseYou haven't given a derivation for "angular work" or "radial work".and so forthAround 50 years ago my colleague Christine and I were building a radiation calorimeter, capable of measuring one microdegree temperature change, using what was then the most advanced analog electronics, programmable phase-locked arbitrary waveform generators, turbomolecular pumps with electronic vacuum gauges, and PID ambient temperature control systems, all either our own design or hot off the manufacturer's next-year catalog. We shared a birthday, so we used to laugh at our daily horoscope. The day we came to switch it all on, we read: "Capricorn - It is better to leave electrical work to an expert."I commend the astrologer's advice to the honorable gentleman: leave SI standards to those who understand physics.
QuoteHow do you fix this?By understanding the meaning of rad, and knowing that v = ds/dt, ω = dθ/dt and s = rθ.
The Terrible Truth About Human Stupidity ? Bonhoeffer?s Forgotten WarningIs stupidity less about a lack of intelligence and more about a refusal to think?In this thought-provoking and educational video essay, we explore theologian and philosopher Dietrich Bonhoeffer?s powerful warning about human stupidity ? a social and psychological phenomenon that goes far beyond individual ignorance.🔎 What you?ll discover:✅ Why even intelligent people can support destructive ideas✅ How groupthink, social pressure and conformity affect the collective psyche✅ Practical tools for maintaining your intellectual independence amid the avalanche of misinformationUsing an in-depth analysis that combines philosophy, psychology, neuroscience and media, we investigate how stupidity can manifest itself in modern societies, fueled by information bubbles, algorithms and ideological manipulations.💡 This video is an invitation to critical thinking, self-awareness, and active resistance to blind conformity ? a timely call in a world increasingly saturated with noise and superficiality.🧠 Key themes:Collective stupidity and individual responsibilityMass manipulation and social behaviorThe human psyche in the face of authority and misinformationBonhoeffer, Hannah Arendt, and the risks of passive thinking🗣️ Bonhoeffer's reflection:?Against stupidity, we are defenseless.?An urgent reminder: resisting organized stupidity is one of the greatest responsibilities of the free individual.💬 Question for you:What belief or idea are you willing to question this week? Comment below ? let's reflect together.👍 If you value content that stimulates the mind and spirit, like, subscribe, and share with someone who is ready to think beyond the obvious.⸻📌 Keywords: human stupidity, psyche, Bonhoeffer, conformism, misinformation, critical thinking, social manipulation, political philosophy, social psychology, collective intelligence, individual responsibility📢 Disclaimer:This video is for educational and informative purposes only. We do not promote or glorify historical regimes, harmful ideologies or any form of intolerance. All references are made for analysis, reflection and learning. We repudiate any expression of hatred, discrimination or violence.
English spelling is broken. Often the letters we write down on the page bear little resemblance to the words we say out loud. Many attempts have been made to fix this, by medieval monks and American presidents. So let's investigate some of these attempts and find out why they failed.Can English spelling be fixed, or is it doomed to remain nightmare for learners? Let's find out.#spelling #english #linguistics==CHAPTERS==0:00 Introduction0:22 The problem with English1:26 Orrmin the monnk5:24 N4mbers for vowels10:13 N8mbers for everything12:35 Noah Webster14:29 Benjamin Franklin15:11 President Theodore Roosevelt17:00 Why change failed14:48 Is spelling changing?19:55 Should it change?
2π rad/s = 1 cycle/second = 1 Hz = 1/s
English spelling is broken.
What belief or idea are you willing to question this week?
Consistency doesn't seem to be the human's particular strength.