The foundation of physics rests upon physical quantities in terms of which the laws of physics are expressed. Therefore, these quantities have to be measured accurately. Among these are mass, length, time velocity, force, density, temperature, electric current, and numerous others.

Physical quantities are often divided into two categories: base quantities and derived quantities. Derived quantities are those whose definitions are based on other physical quantities. Velocity acceleration and force etc. are usually viewed as derived quantities. Base quantities are not defined in terms of other physical quantities. The base quantities are the minimum number of those physical quantities in terms of which other physical quantities can be defined. Typical examples of base quantities are length, mass and time.

The measurement of a base quantity involves two steps: first, the choice of a standard, and second, the establishment of a procedure for comparing the quantity to be measured with he standard so that a number and a unit are determined as the measure of that quantity.

An ideal standard has two principal characteristics: it is accessible and it is invariable. These two requirements are often incompatible and a compromise has to be made between them.

# Base Units

The international system of units known as SI units (systeme international d’Unites) is based on the seven units listed in Table A1.1. These are called basic units, and the particular seven used in the system are chosen for convenience – not out of necessity. Three of the basic units are defined below, some of the others are defined at relevant places in the text.

 Base quantity Unit Name Symbol Mass kiliogram k Length meter m Time second s Electric current ampere A Temperature kelvin K Amounty of substance mole mol Luminous intensity candela cd

# Derived Units

The metre (m) is the unit of length and is equal to 1/299792458 of the distance travelled by light in the vaccum in one second.
The kilogram (kg) is the unit of mass and is equal to the mass of the international prototype kilogram (a platinum-iridium cylinder) kept at sevres, paris.
The second (s) is the unit of time and is the duration of exactly 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of a caesium 133 atom.

Apart from the radian and the steradian, * all the other units used in the system are called derived units. Derived units are formed by multiplication and/or division of one or more basic units without the inclusion of any numerical factors (e.g one coulomb = one ampere X one second). Some derived units are relatively complex when expressed in terms of the basic units, and, for convenience, are given special names (e.g the kg  m2s S-3 A-2  is called the ohm,?. Much used units also have special names (e.g the A s is called the coulomb, C). Those derived units which have special names and are used in this book are listed in Table A1.2. The symbol for a unit which is named after a person has a capital letter.

*The unit of angle (the radian) and the unit of solid angle (the steradian) are officially designated as subsidiary units and can be treated as being either basic or derived as convenience dictates.

 Derived quantity Unit Name Symbol Force newtton N = kgms-2 Pressure pascal Pa=kgm-1s-2 Energy, work joule J = kgm2s-2 Power watt W = kgm2s-3 Frequency hertz Hz = s-1 Charge coulomb C = As Electromotive force volt V = kgm2s-3A-1 Resistance ohm ? = kgm2s-3A-2 Conductance siemens S = kg-1m-2s3A2 Inductance henry H = kgm2s-2A-2 Capacitance farad F = kg-1m-2sA2 Magnetic flux weber Wb = kgm2s-2A-1 Magnetic flux density tesla T = kgs-2A-1

# Prefixes

Prefixces are used with the unit symbols to indicate decimal multiples or submultiples. Most of the standard prefixces are listed in the table below.

 Submultiples Prefix Symbol Multiple Prefix Symbol 10-2 centi c 103 kilo k 10-3 milli m 106 mega M 10-6 micro µ 109 giga G 10-9 nano n 1012 tera T 10-12 pico p 10-15 femto f 10-18 atto a

 Notes 1 cm = 1 X 10-2 1 mm = 1 X 10-3 m 1 cm2 = 1 X 10-4 m2 1 mm2 = 1 X 10-6 m2 1 cm3 = 1 X 10-6 m3 1 mm3 = 1 X 10-9 m3