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From: Terje Slettebø (tslettebo_at_[hidden])
Date: 2003-04-27 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
> > dimensionless quantity. However, in their real-life experience, they
> > 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 SI-representation, 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
> > as a dimension, may be treated like the other dimensions.
> I guess I can't play in that mind-space, 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.



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