My coauthor and I have a (the) solution to an inconsistency in units of measure in rotational mechanics that has induced BIPM to assert that Joule and Newton*meter are not interchangeable units in rotational mechanics(!) See https://www.researchgate.net/publication/342338981. We have not found a journal that will review the article. I believe the main obstacle is that metrologists feel that meters is the "obviously correct" unit of measure for radius of rotation, whereas the principle of general covariance requires that radius of rotation have units meters/radian. We seek a refereed publication that will review the work and publish it. Any suggestions?
I know that the World Journal of Mechanics has published papers on the subject as recently as 2017, possibly more since that time.
Hi Steven, Thank you for the suggestion. I will look them up.
-Richard
Both the BIPM and Richard may benefit from the following considerations, made possible by the introduction of the vector and tensor concepts at the turn of the 19th-20th century.
A physical quantity is not only carrying units with their numerical value, but also a tensorial structure. Scalars like mass, energy are tensors of order 0, so are fully characterized by their magnitude and their units. But other quantities like positions, velocities are vectors, i.e., tensors of order 1, fully characterized by their magnitude and units, in addition to two angles (in 3D space). Angular momenta and moments of force (torques) are actually particular tensors of order 2 with bi-vector structure (oriented 2D surface), so contains implicitly information on their magnitude, units, orientation, and chirality (left-handed or right-handed) of the coordinate system.
So the basic reason one cannot consider energy equivalent to torque are not the units (kg m^2/s^2) but the tensorial structure. A torque includes more information than its mere magnitude and units, i..e. two angles (no unit), and the chirality (+ or -1, no unit).
The same for the scalar action (kg m^2/s) and bi-vector angular momentum.
Hi Daniel, you are tight that the tensor structure drivess the units.
I am presenting that view (which is embedded in the principle of general covariance in math physics).
The conventional answer among engineers seems to be "My eyes tell me that radius is a length, while you are telling me not to believe my lying eyes and the the units for radius are meters/radian. So I believe my eyes."
Thanks,
-Richard
You can send your manuscript in the OPEN PHYSICS journal (Previously Central European journal of Physics). This journal covers wide field of mechanics, physics, etc. Not only that, if the editor finds another journal suitable for publication of your manuscript he/ she will inform you accordingly.
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