This subject has revealed three viewpoints. In USMA 16134 I wrote: >> In this instance I am with the engineers. I would say that >> (N.m/rad) x rad = N.m.
Bill Hooper replied >and I would say > >(N.m) x rad = N.m > >and to hell with the engineers. > >I justify the "disappearance" of the rad by the fact that the rad is equal >to the unitless number 1. (I would even go so far as to suggest that the >substitution of 1 for rad could occur when describing the angle before it is >even substituted into the equation, so that > > (N.m) x rad > >never appears, but the calculation is done as > >(N.m) x (1) = (N.m) > >More specifically, if numbers are used (which they certainly are), an using >a torque of t = 3 N.m and an angle of a = 4 radians, and using E for energy, >I would write > >E = t x a >E = (3 N.m) x (4) = 12 N.m >E = 12 J > >I see no reason for including the radian anywhere in the calculation. > >Regards, >Bill Hooper > >PS I intend all the symbols above to be the magnitudes only of the >quantities, and therefore they are scalar, not vector, quantities. In USMA 16106 Gene Mechtly pointed out that torque is the vector product of two vectors, He pointed out that vector products are not commutative and appeared concerned whether one's vector product is directed above the paper or below it. In USMA 16190 Bill Hooper admitted that torque is a vector but added in USMA 16192: >Our discussion concerned the units of torque. In that discussion, it is only >the magnitude of the torque that is of interest. In any case, the units of >torque should not be modified to include the vector characteristic (or any >other characteristic) of the torque. "The International System of Units" Supplement 2000 in the footnotes to Table 3 says: "(a) The radian and steradian may be used to advantage in expressions for derived units to distinguish between quantities of different nature but the same dimension. Some examplea are given in Table 4. "(b) In practice, the symbols rad and sr are used where appropriate, "(c) In photometry, the name steradian and the symbol sr are usually retained in expressions for units." "2.2.2 ...A derived unit can often be expressed in different ways by combining the names of base units with special names for derived units....In practice, with cerain quantities preference is given to the use of certain special names, or combinations of unit names, in order to facilitate the distinction between different quantities having the same dimension....the SI unit of angular velocity is designated the radian per second rather than the reciprocal second (in this case retaining the word radian emphasizes that angular velocity is equal to 2� times the rotational frequency)." Photometry uses the steradian in the definition of several units. Why the vehement objection to the use of radian in mechanical units expressed by several members of this list? Joseph B.Reid 17 Glebe Road West Toronto M5P 1C8 TEL. 416-486-6071
