Re: Radians, dimensions, & explanations

["Robert W. Harris" <rwharris@CATH-MEM.ORG>]

The definition of the angle is (arc length)/(radius).  Therefore, the labels
on the arc length and the radius will cancel each other out, no label is
left.  It doesn't matter whether you are using inches, centimeters, or
whatevers to measure the arc and radius, providing you use the SAME unit for
both, they will cancel.  Therefore this has no label and doesn't depend upon
the system of measurement being used (like efficiency, or the coefficient of
friction, but we won't go there!)
It seems to me that is sufficient for a high school class explanation.

There was a  much more thorough and technical explanation in The Physics
Teacher within the past year, I think.

Br. Robert W. Harris
Catholic Memorial High School
rwharris@cath-mem.org
http://www.cath-mem.org/cath-mem/physics/contents.htm

-----Original Message-----
From: Mike Wilson <mwilson@COLOSYS.NET>
To: PHYS-L@LISTS.NAU.EDU <PHYS-L@LISTS.NAU.EDU>
Date: Wednesday, December 09, 1998 1:43 PM
Subject: Radians, dimensions, & explanations


> > From <Mike Wilson mwilson@colosys.net>
>
> Each year as I go through angular motion I realize
> I do not have a simple explanation for why radians are a dimensionless
> measurement.
>
> I am always forced back into some discussion of the circumference of
> a circle as 2 pi radi so the distance drops out.
>
> My students routinely seem to have a rather blank expression at this
> explanation.  They are more than willing to just accept "because" as
> an answer.
>
> I hope I can provide a better answer.
>
> Thanks for any ideas or feedback.
>
>
>
> Best Wishes,
>
> Mike Wilson
> mwilson@colosys.net
> Math/Science
> West Grand HS
> Kremmling, Colorado