Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: RADIANS



By accident the whole issue of dimensions has taken on a new meaning for
me based on some work my spouse is doing regarding early use of
wind-tunnels in this country and England. One problem was how to scale
up (pardon me Bob) the wind tunnel measurements to be useful on full
scale aeroplanes, since flight tests in those days were frequently
tragic.
The scaling committee of the National Physical Laboratory at Teddington
included the best minds in England, including as I recall Lord Rayleigh,
the director of the Cavendish Laboratory. Rayleigh wrote articles about
Dimensional Analysis, in which one could construct groups of variables
where were dimensionless, and so could be scaled. This led to a
discussion of whether or not temperature could be written in terms of
mass, length, and time, because of the results from ideal gas
theory. The then head of the National Bureau of Standards wrote an
extensive text on dimensional analysis in which he formalized the logic
and mathematics of the process. The flavor of the paper is the same as
you get from reading Lagrangian mechanics or advanced thermo.

To get back to the issue, I think angle is one of these dimensionless
groups, it has a magnitude, and you can give it a unit so that you can
compare different angles, but in the end it is, as other have said, the
way you scale two lengths, so that if you know the radius you know the
arclength and vice-versa.

I had not realized that this, apparently side-line in my physics course
which was used mostly for checking the accuracy of students
mathematical manipulations, and the physical legitimacy of statements,
had such a noble history.

cheers,

joe

sOn Wed, 29 Nov 2000, Tim O'Donnell wrote:

You can measure lots of things that have no dimensions. For example
the aspect ratio of a rectangle - height/width - has no dimensions.
Similarly for an angular measurement (arc length/radius)

But again that's calculated not measured.
Tim O'Donnell
Instructor of Physics and Chemistry
Celina High School
715 East Wayne Street
Celina, Ohio 45822
(419) 586-8300 Ext 1200 or 1201
odonnt@celina.k12.oh.us

"Chance only favors the prepared mind." - Louis Pasteur