Hi. This is a small utility for see the dimensions of a unit.

dimensions.sm (61 KiB) downloaded 104 time(s).
dimensions.pdf (97 KiB) downloaded 147 time(s).

Best regards.
Alvaro.

Notice that can't find torque.
Torque is just visual popular equivalent of force ... kgf, kN

Wrote

Notice that can't find torque.
Torque is just visual popular equivalent of force ... kgf, kN

Hi. Things don't turns by forces, but by torques. You can't open nor close a door just applying a force, you must to apply a torque equal to some force by it's distance to the axis of rotation, which have dimensions of energy.

Best regards.
Alvaro.

Wrote

Wrote

Notice that can't find torque.
Torque is just visual popular equivalent of force ... kgf, kN

Hi. Things don't turns by forces, but by torques. You can't open nor close a door just applying a force, you must to apply a torque equal to some force by it's distance to the axis of rotation, which have dimensions of energy.

Best regards.
Alvaro.

Judging the physical dimension from base units is not really more than just guessing. Energy and torque are just examples of that. Stress and energy density or frequency and angular velocity are other ones. Such issues frequently pop up in the forum.

Not even speaking of quantities defined by unitless ratios like strain and angle. What about material properties? Even such innocent units like Newtons could be J/m, e.g. line energy in welding.

In a sense you try to guess physical meaning from the mathematical representation. Units in SMath support this process to a really useful extend, but aren't unique.
SMath can't know what the appropriate unit for a result would be. But the user can specify expected units and whether the units match.

A clean solution isn't possible without some sort of quantity tag for variables and constants. The user needs to assign the tag upon definition, either implicitly by assigning a unit, or in case of ambiguity, gets a hint on what the assumption is and how to change that (perhaps in the help text for the unit).
We partially have such tagging with the Delta tag for temperature units to indicate differences of temperatures. But that is a tool-specific solution which isn't obvious for new users It is enforced by the added complexity, that we have different conversion rules based on what the physical meaning is.

A good system for physical dimensions is one that doesn't allow you to add quantities (variable or constant) of different dimensions even if the units match.

Units are just numbers between themselves ...
like saying that π = ln(2) under certain applications.
Under other applications, π = SQRT(2)
Torque = kgf*m native SI = 9.80665 N*m = 1J
.........
so many kgf applied on the wheels * so many km
= so many J = so many liters of diesel fuel = so many $.

Unit Torque.sm (33 KiB) downloaded 75 time(s).