UNITS & DIMENSIONSPHYSICAL QUANTITY: A physical quantity (or "physical magnitude") is a physical property of a phenomenon, body, or substance that can be quantified by measurement.

EXTENSIVE AND INTENSIVE QUANTITIES:

An extensive quantity is equal to the sum of that quantity for all of its constituent subsystems; examples include volume, mass, and electric charge. For instance, if an object has mass m1 and another has mass m2 then a system simply comprising those two objects will have a mass of m1 + m2.

An intensive quantity is independent of the extent of the system; quantities such as temperature, pressure, and density are examples. To illustrate, if two objects having a given temperature are combined, together they still have the same temperature (not twice the temperature).

There are also physical quantities that can be classified as neither extensive nor intensive, for example an extensive quantity with a nonlinear operator applied, such as the square of volume.

UNITS OF MEASUREMENT:

A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention or by law that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of measurement. For example, length is a physical quantity. The metre is a unit of length that represents a definite predetermined length. When we say 10 metres (or 10 m), we actually mean 10 times the definite predetermined length called "metre".

THE INTERNATIONAL SYSTEM OF UNITS:

The International System of Units (abbreviated SI from French: Le Système international d'unités) is the globally accepted and widely used system of measurement, used in both everyday commerce and science. It comprises a coherent system of units of measurement built around seven base units, 22 named and an indeterminate number of unnamed coherent derived units, and a set of prefixes that act as decimal-based multipliers. It is part of the International System of Quantities.

FUNDAMENTAL AND DERIVED UNITS:

FUNDAMENTAL/BASE UNITS: The Système International d’Unités (SI), or International System of Units, defines seven units of measure as a basic set from which all other SI units are derived.

The SI base quantities form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology. However, in a given realization in these units they may well be interdependent, i.e. defined in terms of each other.

The names and symbols of SI base units are written in lowercase (e.g. metre (US English: meter) has the symbol m), except the symbols of those named after persons which are written with an

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initial capital letter (i.e., the kelvin after Lord Kelvin has the symbol K and the ampere after André-Marie Ampère has the symbol A).

Many other units, such as the litre (US English: liter), are formally not part of the SI, but are accepted for use with SI.

Following are the official definitions of the seven base units, as given by BIPM. The links in the first column are to my (possibly) less obscure definitions.

S No. Unit Quantity Definition1 meter (m) distance "The metre is the length of the path travelled by light in

vacuum during a time interval of 1/299 792 458 of a second."

2 kilogram(kg) mass "The kilogram is equal to the mass of the international prototype of the kilogram."

3 second(s) time "The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom."

4 ampere(A) electric current

"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 × 10-7 newton per metre of length."

5 kelvin(K) temperature

"The kelvin is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water."

6 mole(mol) amount of substance

"The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles."

7 candela(cd) intensity of light

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

DERIVED UNITS: All other units is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units. For example, the SI derived unit of area is the square metre (m2), and the SI derived unit of density is the kilogram per cubic metre (kg/m3 or kg m-3). The degree Celsius (see the table below) has a somewhat unclear status, and is arguably an exception to this rule.

The names of SI units are written in lowercase. The symbols for units named after persons, however, are always written with an uppercase initial letter (e.g. the symbol for the hertz is "Hz"; but the symbol for the metre is "m").

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SCALAR & VECTOR QUANTITY:

Scalar Quantity: Scalars are used to describe one dimensional quantity, that is, quantities which require only one number to completely describe them. Examples of scalar quantities are:

Temperature Time Speed Mass Location along a Line

Vector Quantity: Vectors are used to describe multi-dimensional quantities. Multi-dimensional quantities are those which require more than one number to completely describe them. Vectors, unlike scalars, have two characteristics, magnitude and direction. Examples of vector quantities are:

Location in a Plane (2D) Location in Space (3D) Velocity Acceleration Force

DIMENSIONS: In physical terms, dimension refers to the constituent structure of all space and its position in time as well as the spatial constitution of objects within—structures that correlate with both particle and field conceptions, interact according to relative properties of mass—and are fundamentally mathematical in description.

DIMENSIONAL ANALYSIS:

Dimensional analysis is the analysis of the relationships between different physical quantities by identifying their fundamental dimensions (such as length, mass, time, and electric charge) and units of measure (such as miles vs. kilometers, or pounds vs. kilograms vs. grams) and tracking these dimensions as calculations or comparisons are performed. Converting from one dimensional unit to another is often somewhat complex.

Any physically meaningful equation (and any inequality and inequation) must have the same dimensions on the left and right sides. Checking this is a common application of performing dimensional analysis. Dimensional analysis is also routinely used as a check on the plausibility of derived equations and computations. It is generally used to categorize types of physical quantities and units based on their relationship to or dependence on other units

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