Re: when to write radians

[Herb Schulz <herbs@WIDEOPENWEST.COM>]

On 6/30/03 7:42 AM, "Joe Heafner" <heafnerj@VNET.NET> wrote:

> 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. Now, suppose we compare two other linear quantities
> such as the height of two people. Suppose the heights are 5 ft and 6 ft
> (pardon the use of non-SI). Am I correct in stating that in this case,
> the ratio is still dimensionless but will carry no unit (e.g. "radian")
> because no angular measure is involved?
>
> Cheers,
> Joe Heafner

Howdy,

You could give it name - but it would be meaningless to everyone else :-)

Angular measure is inherently a dimensionless quantity (i.e., is not a
non-trivial combination of units of length, time and/or mass) so you need a
unit so that one knows how many there are if you go around once. You can
write equations between the different units so you can easily transform from
one to the other:

1 rotation = 2*\pi radians = 360 degrees = 400 grad .

Good Luck,

Herb Schulz
(herbs@wideopenwest.com)