physics

Physical quantity

Physical quantity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Physical quantity rather than just read about it. In short: A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is a pair of a numerical value and a unit of measurement.

Key takeaways

Physical quantity belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Physical quantity to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Physical quantity from memory before moving on to harder problems.

Reference excerpt

A physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is a pair of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Vector quantities have, besides numerical value and unit, direction or orientation in space.

Principles

Dimensions

The notion of dimension of a physical quantity was introduced by Joseph Fourier in 1822. By convention, physical quantities are organized in a dimensional system built upon base quantities, each of which is regarded as having its own dimension. The dimension of a quantity Z is denoted dim Z or dim(Z).

Kind Some physical quantities are commensurable, meaning that they can be added, subtracted, and compared with one another. To be commensurable, quantities must have the same dimension, but this alone is not sufficient; the quantities must also be the same kind. For example, both kinematic viscosity and thermal diffusivity have dimension of square length per time (units of m2/s), but they are not commensurable. Quantities of the same kind share extra commonalities beyond their dimension and units allowing their comparison (see also: dimensional equivalence).

Unit There is often a choice of unit, though SI units are usually used in scientific contexts due to their ease of use, international familiarity and prescription. For example, a quantity of mass might be represented by the symbol m, and could be expressed in the units kilograms (kg), pounds (lb), or daltons (Da). The unit of a quantity Z is denoted [Z].

Value

Following ISO 80000-1, any value of a physical quantity Z is expressed as the product of a numerical value {Z} (a pure number) and a unit [Z]:

Z = { Z } × [ Z ] {\displaystyle Z=\{Z\}\times [Z]}

The value is sometimes called denominate number or magnitude (although "magnitude" typically refers to the absolute value or vector norm). For example, let Z {\displaystyle Z} be "2 metres"; then, { Z } = 2 {\displaystyle \{Z\}=2} is the numerical value and [ Z ] = m e t r e {\displaystyle [Z]=\mathrm {metre} } is the unit. Conversely, the numerical value expressed in an arbitrary unit can be obtained as:

{ Z } = Z / [ Z ] {\displaystyle \{Z\}=Z/[Z]}

The multiplication sign is usually left out, just as it is left out between variables in the scientific notation of formulas. The convention used to express quantities is referred to as quantity calculus. In formulas, the unit [Z] can be treated as if it were a specific magnitude of a kind of physical dimension: see Dimensional analysis for more on this treatment.

Typography

International recommendations for the use of symbols for quantities are set out in ISO/IEC 80000, the IUPAP red book and the IUPAC green book. For example, the recommended symbol for the physical quantity "mass" is m, and the recommended symbol for the quantity "electric charge" is Q. Physical quantities are normally typeset in italics. Purely numerical quantities, even those denoted by letters, are usually printed in roman (upright) type, though sometimes in italics. Symbols for elementary functions (circular trigonometric, hyperbolic, logarithmic etc.), changes in a quantity like Δ in Δy or operators like d in dx, are also recommended to be printed in roman type. Examples:

Real numbers, such as 1 or √2, e, the base of natural logarithms, i, the imaginary unit, π for the ratio of a circle's circumference to its diameter, 3.14159265... δx, Δy, dz, representing differences (finite or otherwise) in the quantities x, y and z sin α, sinh γ, log x

Support

Scalars

A scalar is a physical quantity that has magnitude but no direction. Symbols for physical quantities are usually chosen to be a single letter of the Latin or Greek alphabet, and are printed in italic type.

Vectors

Vectors are physical quantities that possess both magnitude and direction and whose operations obey the axioms of a vector space. Symbols for physical quantities that are vectors are in bold type, underlined or with an arrow above. For example, if u is the speed of a particle, then the straightforward notations for its velocity are u, u, or u → {\displaystyle {\vec {u}}} .

Tensors

Scalar and vector quantities are the simplest tensor quantities, which are tensors that can be used to describe more general physical properties. For example, the Cauchy stress tensor possesses magnitude, direction, and orientation qualities.

Systems of quantities A system of quantities relates different physical quantities.

Base quantities A limited number of quantities can serve as a basis in terms of which the dimensions of all the remaining quantities of the system can be defined. A set of mutually independent quantities may be chosen by convention to act as such a set, and are called base quantities. The seven base quantities of the International System of Quantities (ISQ) and their corresponding SI units and dimensions are listed in the following table. Other conventions may have a different number of base units (e.g. the CGS and MKS systems of units).

The angular quantities, plane angle and solid angle, are defined as derived dimensionless quantities in the SI. For some relations, their units radian and steradian can be written explicitly to emphasize the fact that the quantity involves plane or solid angles.

Derived quantities

Derived quantities are those whose definitions are based on other physical quantities (base quantities). There are many ISQ derived quantities.

Space Important applied base units for space and time are below. Area and volume are thus, of course, derived from the length, but included for completeness as they occur frequently in many derived quantities, in particular densities.

… excerpt ends here. Continue reading the full article.

Illustrations

Worked examples

Example 1 — a first encounter with Physical quantity

Start with the simplest possible case. Write down what Physical quantity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Physical quantity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Physical quantity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Physical quantity

In research: Physical quantity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Physical quantity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Physical quantity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Physical quantities, so understanding it makes those chapters shorter.
In everyday life: Look for Physical quantity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Physical quantity in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Physical quantity means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Physical quantity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Physical quantity in simple terms?

Why does Physical quantity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Physical quantity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Physical quantity.