[alancalverd]

Torque is defined as rotational counterpart of force.

No it isn't. Torque is defined as the product of tangential force x moment arm, whether or not anything rotates.

Now let's say τ= 1 kg.m²/s²rad = I α and I = 1kg/m². Then

α = 1/s².rad

But on my planet, angular acceleration is measured in rad/s²

[hamdani yusuf (OP)]

Elementary physics- Stead.

Then you should be able to easily spot the problem.

[hamdani yusuf (OP)]

No it isn't. Torque is defined as the product of tangential force x moment arm, whether or not anything rotates.

physics
a force that causes something to turn, or the power of such a force
https://dictionary.cambridge.org/dictionary/english/torque

In physics and mechanics, torque is the rotational analogue of linear force.
https://en.m.wikipedia.org/wiki/Torque

1
: a force that produces or tends to produce rotation or torsion
an automobile engine delivers torque to the drive shaft
also : a measure of the effectiveness of such a force that consists of the product of the force and the perpendicular distance from the line of action of the force to the axis of rotation
2
: a turning or twisting force
https://www.merriam-webster.com/dictionary/torque

How do you define moment arm, if it doesn't rotate?

[hamdani yusuf (OP)]

Now let's say τ= 1 kg.m2/s2rad = I α and I = 1kg/m2. Then

α = 1/s2.rad

But on my planet, angular acceleration is measured in rad/s2

See my previous post on conversion factor between linear and angular quantities.

The table below shows the comparison between angular and linear quantities.

Here are the equations conversion, where d = arclength of the circumference corresponding to rotational angle.
θ = d * (θ/d)
ω = v * (θ/d)
α = a * (θ/d)
I = m * (d/θ)^2
τ = F * (d/θ)
L = p * (d/θ)

Can you now spot your mistake?

[hamdani yusuf (OP)]

Now let's say τ= 1 kg.m2/s2rad = I α and I = 1kg/m2. Then

α = 1/s2.rad

Let's do this in the units of current standard.
τ = 1 kg.m²/s²
I = 1 kg.m²
α = 1/s²

after 1 second,
ω = 1 s/s² = 1/s

1/s = 1 Hz
1/s² = 1 Hz²


Can you spot the mistake?

In our current standard units, the radian can come in and out of existence in basic equations involving rotational quantities.

[hamdani yusuf (OP)]

I think I have enough material to make a video

Please don't pollute the cybersphere with drivel. Leave that to priests, politicians and philosophers.

It is important for any standard to be consistent.
The fact that this inconsistencies have been around for so long suggests that it takes a holistic approach to convince people to fix them. A video enables its viewer to imagine the dynamic model of the rotational system, unlike a paper sheet or static web pages.

The video that I am planning to make will be a distillation of information contained in this thread. I think it's important to first explicitly declare the definitions of important words used in the explanation, following the format of Euclid's Elements and Newton's Principia.
Another thing I want to show is the flaws and inconsistencies in our current standards, and how we were likely to have gotten there.
It would explain the common mistakes people often made in defending the current standard units for rotational quantities.
And finally a proposal to improve the consistency of our standards regarding the rotational quantities.

The video will be linked in my petition, so hopefully people can get a more complete picture of the situation with least effort and time before they decide whether or not they will sign and spread it.

[alancalverd]

How do you define moment arm, if it doesn't rotate?

Force x distance.

We use the concept to load an airplane correctly. There are at least two conventions but the simplest is the American standard. The reference point is the tip of the nose cone, and you simply

1 add all the weights of crew, cargo, fuel, etc to the empty weight of the plane to get takeoff weight, then

2 add each element of weight x distance from the nosecone to get total moment arm

You need TOW < MTOW for the plane to lift off with its specified obstacle clearance, and TMA within limits to ensure full controllability throughout the flight envelope.

All these calcs are done with the plane presumed stationary on a horizontal runway - no rotation involved! 

[alancalverd]

Can you spot the mistake?

Yes. Your error.

Angular velocity ω is always measured in radians/second, and α in rad/sec².

Elementary physics.

[hamdani yusuf (OP)]

Can you spot the mistake?

Yes. Your error.

Angular velocity ω is always measured in radians/second, and α in rad/sec².

Elementary physics.

Not always. Angular velocity in electrical motors and generators, pumps, blowers, compressors, gear boxes are commonly stated in rpm (rotation per minute).

In our current standard units, the radian can come in and out of existence in basic equations involving rotational quantities.

I think it's a bug, not a feature.

[hamdani yusuf (OP)]

Force x distance.

Which distance? How do you determine the actual axis of rotation if it doesn't rotate?

[alancalverd]

Angular velocity in electrical motors and generators, pumps, blowers, compressors, gear boxes are commonly stated in rpm (rotation per minute).

Then you have to apply the appropriate conversion factor of 2π/60 ≈ 0.105 to get rad/sec and hence torque, if that's what you need.

[alancalverd]

Which distance? How do you determine the actual axis of rotation if it doesn't rotate?

Read the rest of reply #266 to see how it's done.

What matters for pitch controllability is that the torque available from the elevator must exceed the static moment arm minus the lift moment arm. It doesn't matter where you choose the reference point as long as  your arithmetic is consistent. Other conventions use the empty center of gravity, which is usually just ahead of the center of lift, but whilst it's OK for single-seat planes it gets complicated when you have passengers or cargo distributed along the fuselage, so the American convention is, I think, less prone to error even though it generates very large numbers.

[hamdani yusuf (OP)]

Angular velocity in electrical motors and generators, pumps, blowers, compressors, gear boxes are commonly stated in rpm (rotation per minute).

Then you have to apply the appropriate conversion factor of 2π/60 ≈ 0.105 to get rad/sec and hence torque, if that's what you need.

After the conversion, can the unit then disappear without a trace?

[hamdani yusuf (OP)]

Read the rest of reply #266 to see how it's done.

Then it's just an assumption, albeit reasonably covering most cases in similar scenarios. It lacks in generality.

[alancalverd]

After the conversion, can the unit then disappear without a trace?

Obviously not. A rotational speed of 27 is meaningless. Revolutions per year? Rads per second? There's a heck of a difference!

[alancalverd]

Then it's just an assumption, albeit reasonably covering most cases in similar scenarios. It lacks in generality.

On the contrary, as long as the reference point is defined, you can calculate a moment arm wherever there's a force and a distance, perpendicular to the line of action, to the reference point.

[hamdani yusuf (OP)]

Here's a list of units for angular distance, according to chatGPT.

Radians are commonly used in mathematics and physics, while degrees, arcminutes, and arcseconds are often used in astronomy and navigation.
Angular distance can be measured in rotations (revolutions, turns). Rotations are often used in engineering, mechanics, and rotational motion physics, especially when dealing with cycles and periodic motion (e.g., gears, wheels, and circular motion in physics).

[hamdani yusuf (OP)]

After the conversion, can the unit then disappear without a trace?

Obviously not. A rotational speed of 27 is meaningless. Revolutions per year? Rads per second? There's a heck of a difference!

Then where does the radian go in the unit of torque?

[hamdani yusuf (OP)]

Then it's just an assumption, albeit reasonably covering most cases in similar scenarios. It lacks in generality.

On the contrary, as long as the reference point is defined, you can calculate a moment arm wherever there's a force and a distance, perpendicular to the line of action, to the reference point.

In the case shown in reply#241  , where is the reference point?
https://www.thenakedscientists.com/forum/index.php?topic=87006.msg740278#msg740278

[alancalverd]

The intended reference point was the vice screw at, say, r₁, the eventual  reference point was the foot of the bench at r₂. Ignoring the mass of the vice, if the bench length was L and it weighed B newton then the applied torque to lift it was Fr₂ > BL/2, roughly.