### QUANTITIES AND UNITS

11 Sep 2009

**A. ****Basic Quantities and Derived Quantities**

In physics there are two kinds of physical quantities, those are basic quantities and derived quantities. Basic quantities are the physical quantities the units of which predetermined, while the derived quantities are the physical quantities which the units of which are derived from basic quantity units.

1. Basic Quantities

To communicate the result of a measurement of a certain physical quantity, a *unit *for the quantity must be defined. In 1960, an international committee agreed on a standard system of units for the fundamental quantities of science, called SI (Systme International). The SI is founded on seven *SI base units* for seven *base quantities* assumed to be mutually independent

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 |

**SI Base Units**

The SI unit system consists of seven base units, with a number of other units derived from those foundations. Below are the base SI units, along with their *precise* definitions, showing why it took so long to define some of them.

Length

The base unit of length;In 1799, the legal standard of length in France became the meter, defined as one tenmillionth of the distance from the equator to the North Pole.

Mass

The SI unit of mass, the kilogram, is defined as the mass of a specific platinumiridium alloy cylinder kept at the International Bureau of Weights and Measures at Svres, France

Time

Before 1960, the time standard was defined in terms of the average length of a solar day in the year 1900. (A solar day is the time between successive appearances of the Sun at the highest point it rea-ches in the sky each day.) The basic unit of time, the second, was defined to be (1/60)(1/60)(1/24) _ 1/86 400 of the average solar day

2. Derived Quantities

Other quantities, called* derived quantities*, are defined in terms of the seven base quantities via a system of quantity equations. The* SI derived units* for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.

Table 2. Examples of SI derived units |
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SI derived unit |
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Derived quantity | Name | Symbol |
---|---|---|

area | square meter | m^{2} |

volume | cubic meter | m^{3} |

speed, velocity | meter per second | m/s |

acceleration | meter per second squared | m/s^{2} |

wave number | reciprocal meter | m^{-1} |

mass density | kilogram per cubic meter | kg/m^{3} |

specific volume | cubic meter per kilogram | m^{3}/kg |

current density | ampere per square meter | A/m^{2} |

magnetic field strength | ampere per meter | A/m |

amount-of-substance concentration | mole per cubic meter | mol/m^{3} |

luminance | candela per square meter | cd/m^{2} |

mass fraction | kilogram per kilogram, which may be represented by the number 1 | kg/kg = 1 |

**A. ****Dimensional Analysis**

The term dimension is used in physics to describe the methods or arrangement of derived quantities from basic quantities. The dimensions of basic quantities is written in a capital letter and put in brackets. Look at the bracket