Re: when to write radians

[Robert Cohen <Robert.Cohen@PO-BOX.ESU.EDU>]

On Tuesday, July 01, 2003 10:38 AM, Joe Heafner wrote:

> I used to think that all dimensionless quantities have 
> radians for units, but I don't think that's quite correct. 
> Radians are only needed if the dimensionless quantity is the 
> measure of an angle.

Stating that one uses radians for angles is overlooking the meaning of
radian.  It isn't simply a dimensionless unit for angle.  Rather, it is
a particular one, i.e., length of arc per length of radius when both are
measured with the same units.

Wouldn't "degree" also be a dimensionless quantity?  Just because it is
dimensionless and refers to an angle does not mean it is equivalent to a
radian.  Suppose we define a smidgen as 1/360 of a meter.  Then a degree
can be defined as the ratio (smidgen of arc)/(m of radius).  Wouldn't
this be a dimensionless quantity?

P.S. Wouldn't the unit conversion "180 degree per radian" also be a
dimensionless quantity?

____________________________________________________
Robert Cohen; 570-422-3428; www.esu.edu/~bbq
East Stroudsburg University; E. Stroudsburg, PA 18301