Re: when to write radians

[Sandin <sandint@NCAT.EDU>]

Hi Joe,
I think you're correct.

I tell my students that the radian is not an SI unit involving mass,
length (since m/m = no unit), time, or current. Rather, it is a tag that
often must be kept in order to tell HOW an angle has been measured.
The sine of 30 deg = the sine of pi/6 rad = the sine of 1/12 revolution,
but the sine 30 deg is NOT equal to the sine of pi/6 deg or the sine of
1/12 deg.

A good example of when the radian is kept and when it can be ignored is in
the simple harmonic motion expression v = (omega)A sin[(omega)t], which
is only correct if the angular frequency omega is expressed in rad/s
(or some other unit of time).
In the (omega)A part, we have ([m/m]/s)m, giving units of m/s for v.
In the sin[(omega)t] part, we have the sine of (rad/s)s = the sine of rad.

Tom Sandin


On Mon, 30 Jun 2003, Joe Heafner 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
>
> -----
> I don't have a Lexus, but I have a Mac. Same thing.