Vector Quantities: Can Unit of Measurement Reveal Vector?

[Char. Limit]

Can someone tell, using the unit of a physical measurement, if the measurement is a vector? For example, without knowing about force, can one tell by the unit kg-m/s^2 that force is a vector?

I'm trying to say, for example, thay since the m in kg-m/s^2 is a vector (for example), the whole thing is a vector... I probably sound dumb...

 

[Neo_Anderson]

Does the unit or system have a magnitude of some sort? Does it have a direction of some sort? If it meets both conditions, it's a vector.

 

[Char. Limit]

Well... let's say I invented a new, unused unit... I'll say m^2/s. Could you tell, just by that unit, if the quantity is a vector?

 

[diazona]

Well... let's say I invented a new, unused unit... I'll say m^2/s. Could you tell, just by that unit, if the quantity is a vector?

No. The units have nothing to do with whether the quantity is a vector or scalar. I could perhaps invent a vector quantity with the units m^2/s and a scalar quantity with the same units. Or even several of each.

Example: take the unit of length, the meter. There is a vector quantity, displacement, and a scalar quantity, distance, that are both measured in meters.

Example 2: Current, measured in amperes, can be a scalar or vector depending on who you ask.

Caveat: for some units, there don't happen to be any meaningful vector quantities associated with them. For example, off the top of my head I can't think of a vector quantity with units of mass. Or time. But there's no mathematical reason that one couldn't be created.

 

[Char. Limit]

Thanks.

 

[mikeph]

I am confusing myself a little. When you say "the velocity is 5 m/s north", you really are saying "the magnitude of the velocity vector is 5 m/s, and the direction is north"- so the actual unit is attributed to the magnitude, a scalar. The vector itself doesn't have a unit, but is composed of a set of scalar components, each with their units. From this perspective, only scalars can have units. I could feasibly construct a vector [x,y] in which x and y are scalars with different units, for example in polar coordinates x is a distance and y is dimensionless (the polar angle, in radians, so a ratio of two distances), then there is no convention I know of how to give this vector a unit.

For me it is meaningless to say the vector has units... the vector gives you the location of a point in whatever space you are talking about, and a point does not have units. The distance in that space to a set of normal planes can have units, however, so each component can have units.
Any disagreement with this view?