Improved Units of Measure in Rotational Mechanics ()
ABSTRACT
The SI
system of units in rotational mechanics yields correct numerical results, but
it produces physically incorrect units of measure in many cases. SI units also
violate the principle of general covariance—the general rule for defining continuous coordinates and units in
mathematics and mathematical physics. After 30+ years of wrestling with these
problems, the ultimate authority on units of measure has declared that
Newton–meter and Joule are not equivalent in rotational mechanics, as they are
in the rest of physics. This article proposes a simple modification to SI units
called “Nonstandard International units” (“NI units”) until a better name is
agreed upon. NI units yield correct numerical results and physically correct
units of measure, and they satisfy the principle of general covariance. The
main obstacle to the adoption
of NI units is the consensus among users that the radius of rotation should have the unit meter
because the radius
can be measured with a ruler. NI units assigned to radius should have units
meter/radian because the radius
is a conversion factor between angular size and circumferential length, as in
arclength = rθ. To manage the social
consensus behind SI units, the author recommends retaining SI units as they are, and informing users who
want correct units that NI units solve the technical problems of SI units.
Share and Cite:
Petti, R. J. (2024) Improved Units of Measure in Rotational Mechanics.
World Journal of Mechanics,
14, 1-7. doi:
10.4236/wjm.2024.141001.
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