Re: when to write radians

[John Barrer <forcejb@YAHOO.COM>]

--- Joe Heafner <heafnerj@VNET.NET> wrote (in part):
> Hi.
> The angle subtended at the center of a circle by an
> arc of that circle
> has a measure, in radians, equal to the ratio of the
> arc length to the
> circle's radius. This ratio is the dimensionless
> ratio of two linear
> quantities, and the "radian" is needed to express
> the measure of the
> angle in some unit.

I would argue that beginning students should be made
to understand that an operational definition of a
radian is not truly dimensionless, but literally
(meters of arc)/(meters of radius). Mathematically
dimensionless, but not operationally. The
"dimensionless" shorthand can all too easily obscure
the physical meaning of a radian.

In a similar vein, explicitly expressing acceleration
as (meters/sec)/(sec) rather than (meters)/(sec)^2 is
far more useful and operationally meaningful to the
beginner even though they are identical
mathematically.  John Barrere

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