
Boost : 
From: Terje Slettebø (tslettebo_at_[hidden])
Date: 20030427 11:32:36
>From: "David Abrahams" <dave_at_[hidden]>
> Terje Slettebø <tslettebo_at_[hidden]> writes:
>
> >>From: "David Abrahams" <dave_at_[hidden]>
> >
> >> Yes. Angle is a dimensionless scalar (length/length). All its
> >> exponents are zero.
> >
> > Yes, Renej (in the posting I replied to) also pointed out that angle is
a
> > dimensionless quantity. However, in their reallife experience, they
found
> > it useful not to have it dimensionless, but instead having it as an
> > additional dimension, to be able to distinguish things like velocity and
> > angular velocity.
>
> They are distinguished!
Yes, they are. After I sent it, I realised that this example  which was in
the original posting  is distinguished, so the issue is to distinguish
between different forms which otherwise has the same SIrepresentation, such
as in this case 1/s (Hz, rad/s, sr/s (steradians), Bq (bequerel)).
> Velocity is l/t and angular velocity is 1/t  the same as frequency.
> Makes perfect sense to me.
Like I said, in OP's case, they wanted to distinguish between them, so that
you for example couldn't add Hz and rad/s.
> > I'm guessing that the answer to my question is, yes, angle, when
expressed
> > as a dimension, may be treated like the other dimensions.
>
> I guess I can't play in that mindspace, because I can't get away from
> what seems to me like a clear truth: angle is dimensionless. If you
> give it dimension, you'll get confusing results (like no relationship
> between angular velocity and frequency).
It certainly would make it easier to make an SI unit library, if they are
treated as dimensionless. However, OP expressed that in practice, it may be
useful to be able to distinguish different units with the same SI
representation. It may not have to be expressed as a dimension, though.
> I wonder what happens to
> physics calculations when frequency is expressed as rad/t?
With or without angle as a dimension this will only mean that this will not,
or will, respectively, be interchangeable for Hz.
Regards,
Terje
Boost list run by bdawes at acm.org, gregod at cs.rpi.edu, cpdaniel at pacbell.net, john at johnmaddock.co.uk