Re: [Units] Incorrect definitions for torque, newton_meter

From: Kostas Savvidis (kotika98_at_[hidden])
Date: 2022-09-04 15:31:37

> On Aug 26, 2022, at 03:27, Albert Dvornik via Boost <boost_at_[hidden]> wrote:
> 
> 
> --------------------
> Hi, all.
> 
> The definitions of boost::units::torque_dimension,
> boost::units::si::torque, boost::units::si::newton_meter and
> boost::units::si::newton_meters seem broken. 

I am not previously familiar with Boost.Units but have always been demanding my students and my kids to use units in all calculations.

Just some random remarks:
1) the very first item on the FAQ in the documentation is:
=======
How does one distinguish between quantities that are physically different but have the same units (such as energy and torque)?
Because Boost.Units includes plane and solid angle units in the SI system, torque and energy are, in fact, distinguishable (see torque).....
=======

2) The paper which someone linked, by Quincey, points out that the formula
sin(x) = x - x^3/6 + x^5/5! - ...
demands that angle is dimensionless. I agree and I think that by itself is a reason to not make radian a unit.
But if you do, then you also have the rule that only radians can be substituted into trig functions, but what to do with exp(x) ? Must x be in radians too ?! (see below)

3) Also, as soon as you make radians a unit, there is another formula that gets f*cked up:
   l = r * theta
arc length is in meters, radius is in meters.
Quincey postulates that the fix is to introduce the unit of radius as meters/radian.
Ridiculous, but kind of logical - a circle of radius equal to 5 m/rad has arc of one radian exactly equalt to 5 meters, but
then immediately he says that even so, the formula for area is screwed:
   S = π * r^2 ?

3) Finally, the planck constant used to be h and these days it is hbar:
h had units of J/Hz
while 
hbar has same units, J*s but is smaller by a factor of 2pi. Why? Because
the unit of hbar is J*s/rad and the unit of h would have been J*s/revolution: in quantum mechanics we have stuff like
exp(-i*E*t/hbar)

All this trouble to prevent the beginner from plugging degrees into trig formulas ? I dont think its worth it.

Cheers,
Kostas