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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:
- time (a particular time)
- potential energy
- mechanical energy