## Contents

## Unit SystemsEdit

### SI Units (Système International d'Unités)Edit

These are the internationally agreed upon units and the ones we will use. Historically these units are based on the metric system which was developed in France at the time of the French Revolution.

Base quantity | Name | Symbol |
---|---|---|

length | meter | m |

mass | kilogram | kg |

time | second | s |

electric current | ampere | A |

thermodynamic temperature | kelvin | K |

amount of substance | mole | mol |

luminous intensity | candela | cd |

All physical quantities have units which can be built from the 7 base units listed in Table 1.1 (incidentally the choice of these seven was arbitrary). They are called base units because none of them can be expressed as combinations of the other six. This is similar to breaking a language down into a set of sounds from which all words are made. Another way of viewing the base units is like the three primary colours. All other colours can be made from the primary colours but no primary colour can be made by combining the other two primaries.

Unit names are always written with lowercase initials (e.g. the metre). The symbols (or abbreviations) of units are also written with lowercase initials except if they are named after scientists (e.g. the kelvin (K) and the ampere (A)).

To make life convenient, particular combinations of the base units are given special names. This makes working with them easier, but it is always correct to reduce everything to the base units. Table 1.2 lists some examples of combinations of SI base units assigned special names. Do not be concerned if the formulae look unfamiliar at this stage — we will deal with each in detail in the chapters ahead (as well as many others)!

It is very important that you are able to say the units correctly. For instance, the **newton** is another name for the **kilogram metre per second squared** (kg·m·s^{−2}}, while the **kilogram metre squared per second squared** ((kg·m^{2}·s^{−2}}) is called the **joule**.

Quantity | Formula | Unit Expressed in | Name of |
---|---|---|---|

Base Units | Combination | ||

Force | m·a |
kg·m·s^{−2} |
N (newton) |

Frequency | s^{−1} |
Hz (hertz) | |

Work & Energy | F·s |
kg·m^{2}·s^{−2} |
J (joule) |

Another important aspect of dealing with units is the prefixes that they sometimes have (prefixes are words or letters written in front that change the meaning). The kilogram (kg) is a simple example: 1 kg is 1000 g or 1×10^{3} g. Grouping the 10^{3} and the g together we can replace the 10^{3} with the prefix k (kilo). Therefore the k takes the place of the 10^{3}. Incidentally the kilogram is unique in that it is the only SI base unit containing a prefix.

There are prefixes for many powers of 10 (Table 1.3 lists a large set of these prefixes). This is a larger set than you will need but it serves as a good reference. The case of the prefix symbol is very important. Where a letter features twice in the table, it is written in uppercase for exponents bigger than one and in lowercase for exponents less than one. **Those prefixes listed in boldface should be learnt.**

Prefix | Symbol | Exponent | Prefix | Symbol | Exponent |
---|---|---|---|---|---|

yotta | Y | 10^{24} |
yocto | y | 10^{−24} |

zetta | Z | 10^{21} |
zepto | z | 10^{−21} |

exa | E | 10^{18} |
atto | a | 10^{−18} |

peta | P | 10^{15} |
femto | f | 10^{−15} |

tera | T | 10^{12} |
pico | p | 10^{−12} |

giga |
G | 10^{9} |
nano |
n | 10^{−9} |

mega |
M | 10^{6} |
micro |
µ | 10^{−6} |

kilo |
k | 10^{3} |
milli |
m | 10^{−3} |

hecto | h | 10^{2} |
centi | c | 10^{−2} |

deca | da | 10^{1} |
deci | d | 10^{−1} |

As another example of the use of prefixes, 1×10^{−3} g can be written as 1 mg (1 milligram).

### Other Unit SystemsEdit

The remaining sets of units, although not used by us, are also internationally recognised and still in use by others. We will mention them briefly for interest only.

#### c.g.s UnitsEdit

In this system the metre is replaced by the centimetre and the kilogram is replaced by the gram. This is a simple change but it means that all units derived from these two are changed. For example, the units of force and work are different. These units are used most often in astrophysics and atomic physics.

#### Imperial UnitsEdit

These units (as their name suggests) stem from the days when monarchs decided measures. Here all the base units are different, except the measure of time. This is the unit system you are most likely to encounter if SI units are not used. These units are used by the Americans and British. As you can imagine, having different units in use from place to place makes scientific communication very difficult. This was the motivation for adopting a set of internationally agreed upon units.

#### Natural UnitsEdit

This is the most sophisticated choice of units. Here the most fundamental discovered quantities (such as the speed of light) are set equal to 1. The argument for this choice is that all other quantities should be built from these fundamental units. This system of units is used in high energy physics and quantum mechanics.

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