The INTERNATIONAL SYSTEM OF QUANTITIES (ISQ) is a system based on
seven base quantities : length , mass , time , electric current ,
thermodynamic temperature , amount of substance , and luminous
intensity . Other quantities such as area , pressure , and electrical
resistance are derived from these base quantities by clear,
non-contradictory equations. The ISQ defines the quantities that are
measured with the SI units and also includes many other quantities
in modern science and technology. The ISQ is defined in the
international standard
The 14 parts of
CONTENTS * 1 Base quantities * 2 Derived quantities * 2.1 Dimensions of derived quantities * 2.2 Logarithmic quantities * 3 References * 4 Further reading BASE QUANTITIES A base quantity is a physical quantity in a subset of a given system of quantities that is chosen by convention, where no quantity in the set can be expressed in terms of the others. The ISQ defines seven base quantities. The symbols for them, as for other quantities, are written in italics. The dimension of a physical quantity does not include magnitude or units. The conventional symbolic representation of the dimension of a base quantity is a single upper-case letter in roman (upright) sans-serif type. BASE QUANTITY SYMBOL FOR QUANTITY SYMBOL FOR DIMENSION SI UNIT length l {displaystyle l} L {displaystyle {mathsf {L}}} metre mass m {displaystyle m} M {displaystyle {mathsf {M}}} kilogram time t {displaystyle t} T {displaystyle {mathsf {T}}} second electric current I {displaystyle I} I {displaystyle {mathsf {I}}} ampere thermodynamic temperature T {displaystyle T} {displaystyle {mathsf {Theta }}} kelvin amount of substance n {displaystyle n} N {displaystyle {mathsf {N}}} mole luminous intensity I v {displaystyle I_{text{v}}} J {displaystyle {mathsf {J}}} candela DERIVED QUANTITIES A derived quantity is a quantity in a system of quantities that is a defined in terms of the base quantities of that system. The ISQ defines many derived quantities. DIMENSIONS OF DERIVED QUANTITIES The conventional symbolic representation of the dimension of a derived quantity is the product of powers of the dimensions of the base quantities according to the definition of the derived quantity. The dimension of a quantity is denoted by L a M b T c I d e N f J g {displaystyle {mathsf {L}}^{a}{mathsf {M}}^{b}{mathsf {T}}^{c}{mathsf {I}}^{d}{mathsf {Theta }}^{e}{mathsf {N}}^{f}{mathsf {J}}^{g}} , where the dimensional exponents are positive, negative, or zero. The symbol may be omitted if its exponent is zero. For example, in the ISQ, the quantity dimension of velocity is denoted L T 1 {displaystyle {mathsf {LT}}^{-1}} . The following table lists some quantities defined by the ISQ. A _quantity of dimension one_ is historically known as a _dimensionless quantity_ (a term that is still commonly used); all its dimensional exponents are zero and its dimension symbol is 1. Such a quantity can be regarded as a derived quantity in the form of the ratio of two quantities of the same dimension. DERIVED QUANTITY SYMBOL FOR DIMENSION plane angle 1 {displaystyle 1} solid angle 1 {displaystyle 1} frequency T 1 {displaystyle {mathsf {T}}^{-1}} force L M T 2 {displaystyle {mathsf {LMT}}^{-2}} pressure L 1 M T 2 {displaystyle {mathsf {L}}^{-1}{mathsf {MT}}^{-2}} velocity L T 1 {displaystyle {mathsf {LT}}^{-1}} area L 2 {displaystyle {mathsf {L}}^{2}} volume L 3 {displaystyle {mathsf {L}}^{3}} acceleration L T 2 {displaystyle {mathsf {LT}}^{-2}} LOGARITHMIC QUANTITIES In the ISQ, the level of a quantity _Q_ is defined as log_r_(_Q_/_Q_0), where _r_ is a specified base and _Q_0 is a specified reference value of the quantity. An example of level is sound pressure level . All levels of the ISQ are derived quantities. REFERENCES * ^ "1.16". _International vocabulary of metrology – Basic and
general concepts and associated terms (VIM)_ (PDF) (3rd ed.).
International Bureau of Weights and Measures (BIPM):Joint Committee
for Guides in Metrology. 2012. Retrieved 28 March 2015.
* ^ _
FURTHER READING * B. N. Taylor, Ambler Thompson, _International System of Units
(SI)_,
* v * t * e SI base quantities BASE QUANTITY QUANTITY SI UNIT NAME SYMBOL Dimension symbol Unit name (symbol) EXAMPLE length l, x, r, (etc.) L metre (m) r = 10 m mass m M kilogram (kg) m = 10 kg time, duration t T second (s) t = 10 s electric current I , i I ampere (A) I = 10 A thermodynamic temperature T Θ kelvin (K) T = 10 K amount of substance n N mole (mol) n = 10 mol luminous intensity Iv J candela (cd) Iv = 10 cd _ SPECIFICATION The quantity (not the unit) can have a specification: T_max = 300 K DERIVED QUANTITY DEFINITION A quantity _Q_ is expressed in the base quantities: Q = f ( l , m , t , I , T , n , I v ) {displaystyle Q=fleft({mathit {l,m,t,I,T,n,I}}mathrm {_{v}} right)} _ DERIVED DIMENSION dim Q_ = L_a_ · M_b_ · T_c_ · I_d_ · Θ_e_ · N_f_ · J_g_ (Superscripts a–g are algebraic exponents, usually a positive, negative or zero integer.) EXAMPLE
SEE ALSO *
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