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Units and measurements Base and derived quantities and units SI base units SI derived units SI prefixes Worked example |
Dimensions Scientific notation Significant figures |
Data
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| Learning Outcomes | ||
|---|---|---|
| After studying this section, you will be familiar with the concepts of physical quantities and units, as well as the SI system of units. | ||
Without a widely accepted system of units of measurement our civilization could not exist. Imagine the chaos if there were no standards for the measurement of mass, length and time, for example.
Scientists identify quantities which describe the natural world. In order to decide how much of a particular quantity a given object has, for example, mass, it is necessary to compare that object to the masses of other objects which have known masses, defined in terms of an agreed standard.
The instrument used is called a balance, shown above. A physical quantity can be defined in terms of the operations necessary to measure it. For example, the length of an object can be determined by comparing it to an object of known length, such as a ruler (see examples of physical quantities).
A unit is an established standard for a physical quantity against which particular examples of that physical quantity can be compared. The act of comparing a physical quantity to a unit is called measurement and the measure of a particular physical quantity is the ratio of that physical quantity to the unit.
The measure is a numerical value. When we calculate, we manipulate the measure, not the physical quantity.
Physical quantities are related to one another by mathematical equations, for example:
velocity = displacement / time.
Some physical quantities are chosen as base quantities. Other physical quantities are obtained from the base quantities using the appropriate algebraic relationships and these are called derived quantities .
Base quantities are said to have base units and derived quantities have derived units. For example, if displacement and time are chosen to be base quantities, then velocity is a derived quantity:
By international convention the following seven physical quantities are chosen for use as dimensionally independent base quantities:
| Physical Quantity | Symbol for the Quantity |
|---|---|
| length | l |
| mass | m |
| time | t |
| electric current | I |
| thermodynamic temperature | T |
| luminous intensity | Iv |
| amount of substance | n |
In South Africa, the International System of Units (which is abbreviated "SI", from the French "le Système International d' Unités") as defined by the International Standards Organization is used. SI units are widely accepted and are established by law in most countries. The SI base units are shown in the table below. (Clicking on a name will take you to its definition).
| BASE UNITS | ||
|---|---|---|
| Physical Quantity | Name of Unit | Symbol |
| length | metre | m |
| mass | kilogram | kg |
| time | second | s |
| electric current | ampere | A |
| temperature | kelvin | K |
| luminous intensity | candela | cd |
| amount of substance | mole | mol |
All SI units that are not base units are expressed as combinations of the base units.
| SOME EXAMPLES OF DERIVED SI UNITS | ||
|---|---|---|
| Physical Quantity | SI Unit | Symbol |
| angle | radian | rad |
| solid angle | steradian | sr |
| area | square metre | m2 |
| volume | cubic metre | m3 |
| density | kilogram per cubic metre | kg.m-3 |
| speed | metre per second | m.s-1 |
| acceleration | metre per second squared | m.s-2 |
| concentration | mole per cubic metre | mol.m-3 |
Some derived units, shown in the table below) are given special names: (Clicking on a name will take you to its definition).
| SOME DERIVED SI UNITS WITH SPECIAL NAMES | ||
|---|---|---|
| Physical Quantity | Name of Unit | Symbol |
| energy | joule | J |
| force | newton | N |
| pressure | pascal | Pa |
| power | watt | W |
| electric charge | coulomb | C |
| electric potential difference | volt | V |
| electric resistance | ohm | W |
| frequency | hertz | Hz |
| SI Prefixes | Remarks | ||
|---|---|---|---|
| Multiple | Prefix | Symbol | |
|
10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1 10 102 103 106 109 1012 1015 1018 1021 1024 |
yocto zepto atto femto pico nano micro milli centi deci deca hecto kilo mega giga tera peta exa zetta yotta |
y z a f p n µ m c d da h k M G T P E Z Y |
Decimal multiples are formed by adding prefixes to the name of the SI unit. This avoids having to use cumbersome numbers of digits. It is considered good practice to use prefixes representing 10 raised to a power which is a multiple of 3. For example, 100 ms is preferable to 10 cs or 1 ds. For historical reasons, some multiples of SI units are given special names. While these units are not part of the SI, they are precicely defined in terms of SI units, as shown in the table below. |
| Physical Quantity | Name of Unit | Symbol | Definition | Remarks |
| length | ångstrom | Å | 10-10 m | Prefixes are added to the unit name, and written as one word, e.g. megawatt. Compound prefixes such as millimicrometres are not used. In the case of derived units, only one unit takes a prefix. We write km.s-1 and not mm.µs-1. |
| volume | litre | l | 10-3 m3 | |
| mass | tonne | t | 103 kg | |
| pressure | bar | bar | 105 Pa | |
| time | minute hour day |
min h d |
60 s 3600 s 86400 s |
The measure of a physical quantity is a number equal to the physical quantity divided by the unit.
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For example, if you pay R120 for a book, the amount paid is the physical quantity, the unit of currency is the rand (1 R) and the measure is the number 120. |
| Quantity | Dimensions | Quantity | Dimensions |
| length | [L] | force | [MLT-2] |
| area | [L2] | pressure | [ML-1T-2] |
| volume | [L3] | energy/work | [ML2T-2] |
| density | [ML-3] | power | [ML2T-3] |
| speed | [LT-1] | electric charge | [IT] |
| acceleration | [LT-2] | electric potential difference | [ML2T-3I-1] |
| momentum | [MLT-1] | electric resistance | [ML2T-3I-2] |
SI unit of length: metre - The metre is the the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.
SI units of mass: kilogram - The kilogram is the mass of the international prototype kilogram (a platinum-iridium cylinder) kept at the Bureau International des Poids et Mesures at Sèvres in France.
SI unit of time: second - The second is the duration of 9 192 631 770 periods of exactly 9 192 631 770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium-133 atom at a temperature of 0 K.
SI unit of electric current: ampere - The ampere is the constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross section, and placed 1 metre apart in a vacuum, would produce be tween these conductors a force equal to 2 x 10-7 newton per metre of length.
SI unit of thermodynamic temperature (or absolute temperature): kelvin - The kelvin is the fraction 1/273.16 (exactly) of the thermodynamic temperature of the triple point of water.
SI unit of luminous intensity candela - 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. .
SI unit of amount of substance mole - The mole is the quantity of substance that contains the same number of elementary entities (atoms, molecules, ions, electrons or particles, depending on the substance) as there are atoms in 0.012 kilograms of pure carbon-12; this number (NA) is approximately equal to 6.02214199×1023.
SI unit of plane angle: radian - The radian is the angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle. There are 2p radians in a circle.
SI unit of solid angle angle: steradian - The steradian is the solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2. There are 4p steradians on a sphere.
SI derived unit of energy: joule - The joule is the work done when the point of application of a force of one newton (1N) is displaced through a distance of one metre (1m) in the direction of the force.
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| J | m2.kg.s-2 | N.m |
SI derived unit of force: newton - The newton is that force which, when applied to a body with a mass of one kilogram (1kg), gives it an acceleration of one metre per second squared (1 m.s-2).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| N | m.kg.s-2 | J.m-1 |
SI derived unit of pressure: pascal - The pascal is the pressure which results when a force of one newton (1N), is applied evenly and perpendicularly to an area of one square metre (1 m2).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| Pa | m-1.kg.s-2 | N.m2, J.m-3 |
SI derived unit of power: watt - The watt is the power which results in the production of energy at the rate of one joule per second (1 J.s-1).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| W | m2.kg.s-3 | J.s-1 |
SI derived unit of electric charge: coulomb - The coulomb is the quantity of electric charge transported in one second (1s) by a current of one ampere (1A).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| C | s.A | A.s |
SI derived unit of electric potential difference: volt - The volt is the potential difference between two points of a conduction wire carrying a constant current of one ampere (1A), when the power dissipated between these points is one watt (1W).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| V | m2.kg.s-3.A-1 | J.A-1.s-1, J.C-1, W.A-1 |
SI derived unit of electric resistance: ohm - The ohm is the electric resistance between two points of a conductor when a constant potential difference of one volt (1V), applied between these two points, produces a current of one ampere (1A), the conductor not being the source of any electromotive force.
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| W | m2.kg.s-3.A-2 | V.A-1 |
SI derived unit of frequency: hertz - The hertz is the frequency of a periodic phenomenon of which the period is one second (1s).
| Symbol | Definition of SI Unit | Equivalent Form of SI Unit |
| Hz | s-1 |
Glossary