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Base Units, Derived Units and Physical Dimensions

In terms of measurement, a physical quantity is any 'quantifiable aspect' of the physical world, such as time, distance, velocity, mass, temperature, energy, and weight. 'Units' are used to quantify their magnitude - say how much of that quantifiable aspect we are dealing with!

The dimension of a physical quantity can be expressed as a product of the basic physical dimensions length, mass, time, electric charge, and absolute temperature, represented by sans-serif roman symbols L, M, T, Q, and Θ, respectively, each raised to a rational power. Using these dimensions to analyse equations were part of the A Level syllabus for a long time. You will find old questions on the subject of dimensional analysis.

The SI standard recommends the usage of the following dimensions and corresponding symbols: length (L), mass (M), time (T), electric current (I) (which under the old system would have been Q/T), absolute temperature Θ, amount of substance - number of moles (N) and luminous intensity (J). These are the ones that current syllabuses will refer to.

A base quantity is one of a conventionally chosen subset of physical quantities, where no quantity in the subset can be expressed in terms of the others.

Many of these quantities are related to each other by various physical laws, and as a result the units of a quantities can be generally be expressed as a product of powers of other units; for example, momentum is mass multiplied by velocity, while velocity is measured in distance divided by time. Therefore momentum has the dimensions M L T-1

Any quantities that can be expressed only in terms of the base units are called derived quantities

Base Units

Symbol of Unit Name of Unit Name of Quantity Dimension Symbol  
A ampere current I

The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per metre of length.

cd candela luminosity J

The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz, that has a radiant intensity in that direction of 1/683 watts per steradian.

a steradian is a unit of solid angle
K kelvin thermodynamic temperature Θ

The kelvin, unit of thermodynamic temperature, is the fraction 1 ​⁄ 273.16 of the thermodynamic temperature of the triple point of water.
kg kilogram   M

The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
m metre   L

The metre is the length of the path travelled by light in vacuum during a time interval of 1 ​⁄ 299792458 of a second
mol mole amount of substance N

T.he mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of unbound atoms of carbon 12, at rest and in their ground state.
s second   T

The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest at a temperature of 0K.