units and dimesions

[Mark Sylvester <msylvest@spin.it>]

> WHAT?! Need I say *magnitude* of the torque? I consider this statement to
> be manifestly incorrect. I have heard some (old) teachers like to express
> energy in foot pounds and torque in pound feet, but the dimensions are
> certainly the same. I've heard the same thing said of temperatures
> (degrees Celsius) and temperature changes (Celsius degrees), but those
> dimensions are also the same.

Yes, but "temperature" and "temperature change" are the same thing
physically, and have the same units. Torque and work are not, and have
different units.

> Torque, work, heat, and energy all have the
> same dimensions (M L^2 T^-2). They may be expressed in different units,
> but that does not change the fact of their dimensionality.
>
> Leigh

Could you clarify the difference between units and dimensions for me?
Without thinking about it more deeply, I have assumed the the torque/work
case implies that there is a dimensional difference between "parallel
metres" and "perpendicular metres", i.e. between the result of a dot product
and of a cross product. Can quantities have the same dimensions and yet be
completely different physically?

Mark.
Mark Sylvester
UWCAd, Duino, Trieste, Italy.