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h1. Scalar
{excerpt}A quantity that does not have a direction associated with it.{excerpt}
h3. Negative Scalars
It is important to note that some scalar quantities can be negative. For instance, money is a scalar. You cannot earn "$5 east" or "$5 at 60° south of west". You can, however, owe someone money. Suppose you are a student with $10,000 in loans and no appreciable assets. You might then say your net worth is -- $10,000. The negative sign attached to a scalar functions very differently than the negative sign of a one-dimensional vector. When comparing vectors, we usually compare magnitudes. Thus, a velocity of 50 m/s *west* might be denoted as -- 50 m/s, but it is still larger than a velocity of 20 m/s *east*. A net worth of -- $10,000 is certainly _*not*_ larger than a net worth of $5,000!
Some examples of scalars that are constrained to be positive are:
* mass
* _elapsed_ time
* distance
* speed
* [kinetic energy]
* thermal energy
Some examples of scalars that can be negative are:
* [potential energy]
* [mechanical energy]
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Definition
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A quantity that does not have a direction associated with it. |
Discussion
It is important to note that some scalar quantities can be negative. For instance, money is a scalar. You cannot earn "$5 east" or "$5 at 60° south of west". You can, however, owe someone money. Suppose you are a student with $10,000 in loans and no appreciable assets. You might then say your net worth is – $10,000. The negative sign attached to a scalar functions very differently than the negative sign of a one-dimensional vector. When comparing vectors, we usually compare magnitudes. Thus, a velocity of 50 m/s west might be denoted as – 50 m/s, but it is still larger than a velocity of 20 m/s east. A net worth of – $10,000 is certainly not larger than a net worth of $5,000.
Some examples of scalars that are constrained to be positive are:
- mass
- elapsed time
- distance
- speed
- kinetic energy
- thermal energy
Some examples of scalars that can be negative are:
...