Vector Quantities: Can Unit of Measurement Reveal Vector?

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Discussion Overview

The discussion revolves around whether the unit of a physical measurement can indicate if that measurement is a vector quantity. Participants explore the relationship between units, magnitude, and direction, and consider hypothetical units to illustrate their points.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions if the unit kg-m/s² can reveal that force is a vector, suggesting that the presence of a vector unit implies the entire measurement is a vector.
  • Another participant proposes that if a unit has both magnitude and direction, it qualifies as a vector.
  • A hypothetical unit, m²/s, is introduced to examine whether it can be classified as a vector based solely on its unit.
  • It is argued that units alone do not determine if a quantity is a vector or scalar, as the same units can apply to both types of quantities. Examples include displacement (vector) and distance (scalar), both measured in meters.
  • Participants note that some units may not have meaningful vector quantities associated with them, such as mass or time, but theoretically, vector quantities could be created for any unit.
  • One participant expresses confusion about the attribution of units to vectors, suggesting that only scalars can have units and that vectors are composed of scalar components, each with their own units.
  • The idea is raised that a vector does not possess units itself but rather indicates a location in space, while the components of that vector can have units.

Areas of Agreement / Disagreement

Participants express differing views on whether units can indicate vector status, with some arguing that units do not determine vector or scalar classification, while others suggest that the presence of magnitude and direction is key. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Limitations include the ambiguity in defining vector quantities based solely on units, and the potential for creating new vector quantities with unconventional units. The discussion also highlights the complexity of how units relate to physical concepts.

Char. Limit
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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...
 
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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.
 
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?
 
Char. Limit said:
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.
 
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Thanks.
 
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?
 
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