# SI Units

Units

The system of units used in engineering and science is the Syste`me Internationale d’Unite´s (International system of units), usually abbreviated to SI units, and is based on the metric system. This was introduced in 1960 and is now adopted by the majority of countries as the official system of measurement.

The basic units in the S.I. system are listed below with their symbols:

Prefixes

S.I. units may be made larger or smaller by using prefixes that denote multi- plication or division by a particular amount. The six most common multiples, with their meaning, are listed below:

Length, area, volume and mass

Length is the distance between two points. The standard unit of length is the metre, although the centimetre, cm, millimetre, mm and kilometre, km, are often used.

1 cm D 10 mm, 1 m D 100 cm D 1 000 mm and 1 km D 1 000 m

###### Area is a measure of the size or extent of a plane surface and is measured by multiplying a length by a length. If the lengths are in metres then the unit of area is the square metre, m2

Conversely, 1 cm2 D 10ð4 m2 and 1 mm2 D 10ð6 m2

Volume is a measure of the space occupied by a solid and is measured by multiplying a length by a length by a length. If the lengths are in metres then the unit of volume is in cubic metres, m3

Derived SI Units

Derived SI units use combinations of basic units and there are many of them. Two examples are:

Velocity - metres per second (m/s)

Acceleration - metres per second squared (m/s2 )

##### Charge

The unit of charge is the coulomb (C) where one coulomb is one ampere second. (1 coulomb D 6.24 ð 1018 electrons). The coulomb is defined as the quantity of electricity which flows past a given point in an electric circuit when a current of one ampere is maintained for one second. Thus,

where I is the current in amperes and t is the time in seconds.

Force

The unit of force is the newton (N) where one newton is one kilogram metre per second squared. The newton is defined as the force which, when applied to a mass of one kilogram, gives it an acceleration of one metre per second squared. Thus,

where m is the mass in kilograms and a is the acceleration in metres per second squared. Gravitational force, or weight, is mg, where g D 9.81 m/s2

##### Work

The unit of work or energy is the joule (J) where one joule is one newton metre. The joule is defined as the work done or energy transferred when a force of one newton is exerted through a distance of one metre in the direction of the force. Thus

where F is the force in newtons and s is the distance in metres moved by the body in the direction of the force. Energy is the capacity for doing work.

##### Power

The unit of power is the watt (W) where one watt is one joule per second. Power is defined as the rate of doing work or transferring energy. Thus,

Electrical potential and e.m.f.

The unit of electric potential is the volt (V), where one volt is one joule per coulomb. One volt is defined as the difference in potential between two points in a conductor which, when carrying a current of one ampere, dissipates a power of one watt, i.e.

A change in electric potential between two points in an electric circuit is called a potential difference. The electromotive force (e.m.f.) provided by a source of energy such as a battery or a generator is measured in volts.