A brief description of physical quantities
According to James Clerk Maxwell’s paper on “Mathematical classification of physical quantity”, there are physical and mathematical quantities.
Physical quantities are measurable with analogy in the physical reality. For example, you can measure another person’s height with the unit of your palm size or measure “mass” with kilograms. Physical quantities are usually belonged to the old science that are due to reduce into mathematical forms.
Mathematical quantities agree with physical quantities in their mathematical forms. Mathematical quantities may not be measurable, but one could calculate them based on physics theories and equations.
Another example from Maxwell’s paper: When describing kinetic energy as multiplication of “mass” and “square of velocity”, it can be described as dot product of “momentum” and “velocity” for representing in their mathematical quantities instead of using physical quantities (like mass).
Let’s look at the meaning of words from Oxford dictionary:
“Physical”
- Relating to the body as opposed to the mind.‘a range of physical and mental challenges’More example sentencesSynonyms1.1 Involving bodily contact or activity.‘less physical sports such as bowls’‘a physical relationship’More example sentencesSynonyms
- Relating to things perceived through the senses as opposed to the mind; tangible or concrete.‘the physical world’More example sentences
- Relating to physics or the operation of natural forces generally.
“Quantity”
- The amount or number of a material or abstract thing not usually estimated by spatial measurement.‘the quantity and quality of the fruit can be controlled’More example sentences
1.1 count noun
A certain, usually specified, amount or number of something.‘a small quantity of food’‘if taken in large quantities, the drug can result in liver failure’
1.2 often quantities.
A considerable number or amount of something.‘she was able to drink quantities of beer without degenerating into giggles’mass noun ‘many people like to buy in quantity’More example sentences - Phonetics
The perceived length of a vowel sound or syllable.Example sentences - Mathematics Physics
A value or component that may be expressed in numbers.
For the context of physical sciences, where we study objects around us, the second definition of “physical” and first definition of “quantity” seem to be meaningful. Hence combining these two, a physical quantity, I think, is a measure of (associating a number with) a phenomenon that is observed (or known) via the five senses of man or animal.
Typically we divide physical quantities into two broad categories: base quantities and derived quantities.
Base quantities are those quantities from which all others are obtained. Examples include mass, length, time, etc. Derived quantities are quantities obtained from some combination of one or more base quantity. Examples include velocity (length divided by time), etc.
Besides that we divide physical quantities into another set of categories: scalar quantities and vector quantities.
Scalar quantities are quantities that have some value only. Vector quantities have both a value and a direction component. So mass is a scalar quantity but weight (which is a force) is a vector quantity because it acts downward (i.e. it has a direction)
According to James Clerk Maxwell’s paper on “Mathematical classification of physical quantity”, there are physical and mathematical quantities.
Physical quantities are measurable with analogy in the physical reality. For example, you can measure another person’s height with the unit of your palm size or measure “mass” with kilograms. Physical quantities are usually belonged to the old science that are due to reduce into mathematical forms.
Mathematical quantities agree with physical quantities in their mathematical forms. Mathematical quantities may not be measurable, but one could calculate them based on physics theories and equations.
Another example from Maxwell’s paper: When describing kinetic energy as multiplication of “mass” and “square of velocity”, it can be described as dot product of “momentum” and “velocity” for representing in their mathematical quantities instead of using physical quantities (like mass).
Let’s look at the meaning of words from Oxford dictionary:
“Physical”
- Relating to the body as opposed to the mind.‘a range of physical and mental challenges’More example sentencesSynonyms1.1 Involving bodily contact or activity.‘less physical sports such as bowls’‘a physical relationship’More example sentencesSynonyms
- Relating to things perceived through the senses as opposed to the mind; tangible or concrete.‘the physical world’More example sentences
- Relating to physics or the operation of natural forces generally.
“Quantity”
- The amount or number of a material or abstract thing not usually estimated by spatial measurement.‘the quantity and quality of the fruit can be controlled’More example sentences
1.1 count noun
A certain, usually specified, amount or number of something.‘a small quantity of food’‘if taken in large quantities, the drug can result in liver failure’
1.2 often quantities.
A considerable number or amount of something.‘she was able to drink quantities of beer without degenerating into giggles’mass noun ‘many people like to buy in quantity’More example sentences - Phonetics
The perceived length of a vowel sound or syllable.Example sentences - Mathematics Physics
A value or component that may be expressed in numbers.
For the context of physical sciences, where we study objects around us, the second definition of “physical” and first definition of “quantity” seem to be meaningful. Hence combining these two, a physical quantity, I think, is a measure of (associating a number with) a phenomenon that is observed (or known) via the five senses of man or animal.
Typically we divide physical quantities into two broad categories: base quantities and derived quantities.
Base quantities are those quantities from which all others are obtained. Examples include mass, length, time, etc. Derived quantities are quantities obtained from some combination of one or more base quantity. Examples include velocity (length divided by time), etc.
Besides that we divide physical quantities into another set of categories: scalar quantities and vector quantities.
Scalar quantities are quantities that have some value only. Vector quantities have both a value and a direction component. So mass is a scalar quantity but weight (which is a force) is a vector quantity because it acts downward (i.e. it has a direction)
