Joe Reid wrote:
> How can one denote the distinction between a newton metre as the unit to
> meassure energy and the newton metre as the unit to measure torque?

Why does one need to?

In context it is clear that If a newton-metre is used to describe an energy,
then it is an energy unit (and may be called a joule), whereas if a
newton-metre is used to describe a torque then it is a torque unit (and may
not be called a joule).

That is not difficult.

Joe also wrote:
> We evidently need a way to denote whether a quantity is a scalar or a
> vector quantity.

Yes, but it is not the job of the unit to do so.

Any quantity being measured or calculated is defined so it is either a
scalar or a vector. (Energy is defined in such a way that it must be a
scalar and torque so it must be a vector*.) To know whether something is a
scalar or a vector one needs to know the definition of the quantities with
which he/she is working. If you don't know the complete definition of the
quantity you are talking about, you literally "don't know what you're
talking about".

Regards,
Bill Hooper

*There are times when vector quantities can be used as if they are scalars.
When all the vectors in question are in the same direction, they add as if
they are scalars (added algebraically, taking into account the fact that
some may be positive and others negative).

Torques are often treated this way at an elementary level. When it is
possible and convenient to ignore the vector (direcional) characteristic of
the torque, there would be unnecessary additional complication if the torque
unit were to be modified in some way to indicate its vector character.

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Keep It Simple!
Make It Metric!
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