You can not think of Physics without measurement. We always measure in Physics. What do we measure? We measure a physical quantity. How do we measure? By comparing with a unit of a physical quantity.

We learn what physical quantities mean, the relationship of physical quantities and SI units. We begin by understanding physical quantities with examples and list SI base units and also unit prefixes.

## Physical Quantity

A number which can describe the physical property of a material or a physical phenomenon quantitatively is called physical quantity.

The most fundamental physical quantities can only be defined if you know how to measure them. Such a definition is called operational definition.

If you want to define the fundamental physical quantities such as length, mass and time, you must know how to measure them.

When you measure any physical quantity you must compare it with a particular standard of that physical quantity called unit. You compare with the unit of a physical quantity to measure that physical quantity.

You have a book and you try to find how long or how wide the book is. The measure of how long is length and that of how wide is breadth (width). These two things length and breadth are the physical quantities of the book.

An object can be described by its physical quantities. If you have a ball, the ball is an object and you can describe the ball by its weight, radius, mass etc.

If you are measuring the radius of a ball, the ball is an object and its radius is a physical quantity. Mass of the ball is another physical quantity. You can quantitatively describe the properties of an object by physical quantities.

The base quantities such as length, mass and time are the fundamental ones which do not depend on other quantities. The derived quantities are derived from the base quantities such as area, volume speed etc.

The physical quantities with direction called vectors and those without direction are called scalars.

## SI Units

How do you measure the length of a book? You need to make some standards of length to say the book has this much length. And those standards you use to give the physical quantities a measurable value are the units. Now you can say the book has this much length using your length standard.

For example, you made a stick of a certain length and measured other lengths with that stick and found the length of your bed to be five times that stick. So here the length of the stick you made recently is your temporary length standard (you used it to measure other lengths).

When we make a standard to define a physical quantity, that becomes a unit. Notice that you can give your own standard to any physical quantity, for example if you made the period of a particular pendulum to be your time standard and calculated other time periods like day, month or year, that time period will be based on your own time standard.

Anyone is free to make any standards of units, so it's very important to define universal standards (the same standards in the entire world) of units called SI units (*system international* units). Now we learn how some SI units of some fundamental physical quantities like time, length and mass are defined

### SI Unit of Time

The SI unit of time is **second** denoted by letter **s** which is the time period equal to 9192631770 times the period of vibration of radiation from caesium-133 atom.

We use this standard to measure other time intervals or periods. For example, a particular time period is 1s, 21s, 3s, 15s and so on.

### SI Unit of Length

The SI unit of length is **meter** and denoted by the letter **m**. It is the distance the light travels in 1/2299792458 second.

This standard of length is used to measure other lengths. For example the length of a particular rod is 1m, 5m, 2m and so on.

### SI Unit of Mass

The SI unit of mass has the name **kilogram** and denoted by **kg**.

The the SI unit of mass is the mass of a particular alloy of platinum and iridium kept at the International Bureau of Weights and Measures at Severs, near Paris, France. We calculate the mass of a physical quantity using this standard such as 1kg, 2kg, 32kg etc.

In addition of to the three SI base units we recently described, there are other four SI base units which are kelvin (K) for temperature, ampere (A) for electric current, candela (cd) for luminocity and mole (mol) for amount of substance.

There are also other units other than the SI units used in specific regions of the world. We will only consider the SI units here. There are two types of SI units - one type is SI base units and another is SI derived units. The following table shows 7 SI base units and their corresponding physical quantities.

SI Unit | Symbol | Physical Quantity |
---|---|---|

meter | m | length |

second | s | time |

kilogram | kg | mass |

kelvin | K | temperature |

ampere | A | current |

candela | cd | luminous intensity |

mole | mol | amount of substance |

The 7 SI base units in the above table can be used to derive all other SI units called SI derived units. For example the SI unit of speed is the SI derived unit using two base units meter and second, that is meters per second (m/s).

The two units radian for plane angle and steradian for solid angle are neither SI base units nor SI derived units. These two were expressed as SI supplementary units and don't hold the agreement to be SI base units yet. They are more likely considered as SI derived units.

## Unit Prefixes

Some prefixes can be used with units to define new units. The table below shows the prefixes that can be used with units.

Prefix | Prefix Symbol | Numerical Value | Examples of Meter |
---|---|---|---|

yotta | Y | ${{10}^{24}}$ | 1Ym = 1 yottameter = ${{10}^{24}}$m |

zetta | Z | ${{10}^{21}}$ | 1Zm = 1 zettameter = ${{10}^{21}}$m |

exa | E | ${{10}^{18}}$ | 1Em = 1 exameter = ${{10}^{18}}$m |

peta | P | ${{10}^{15}}$ | 1Pm = 1 petameter = ${{10}^{15}}$m |

tera | T | ${{10}^{12}}$ | 1Tm = 1 terameter = ${{10}^{12}}$m |

giga | G | ${{10}^{9}}$ | 1Gm = 1 gigameter = ${{10}^{9}}$m |

mega | M | ${{10}^{6}}$ | 1Mm = 1 megameter = ${{10}^{6}}$m |

kilo | k | ${{10}^{3}}$ | 1km = 1 kilometer = ${{10}^{3}}$m |

deci | d | ${{10}^{-1}}$ | 1dm = 1 decimeter = ${{10}^{-1}}$m |

centi | c | ${{10}^{-2}}$ | 1cm = 1 centimeter = ${{10}^{-2}}$m |

milli | m | ${{10}^{-3}}$ | 1mm = 1 millimeter = ${{10}^{-3}}$m |

micro | $\mu $ | ${{10}^{-6}}$ | 1$\mu $m = 1 micrometer = ${{10}^{-6}}$m |

nano | n | ${{10}^{-9}}$ | 1nm = 1 nanometer = ${{10}^{-9}}$m |

pico | p | ${{10}^{-12}}$ | 1pm = 1 picometer = ${{10}^{-12}}$m |

femto | f | ${{10}^{-15}}$ | 1fm = 1 femtometer = ${{10}^{-15}}$m |

atto | $a$ | ${{10}^{-18}}$ | 1$a$m = 1 attometer = ${{10}^{-18}}$m |

zepto | z | ${{10}^{-21}}$ | 1zm = 1 zeptometer = ${{10}^{-21}}$m |

yocto | y | ${{10}^{-24}}$ | 1ym = 1 yoctometer = ${{10}^{-24}}$m |

The examples of length are shown in above table. Some examples of mass are time are given in below table.

Mass | Time |
---|---|

1 microgram ($\mu$g) = $10^{-9}$kg | 1 nanosecond (ns) = ${{10}^{-9}}\text{s}$ |

1 miligram (mg) = $10^{-6}$kg | 1 microsecond ($\mu $s) = ${{10}^{-6}}$s |

1 gram (g) = $10^{-3}$kg | 1 millisecond (ms) = ${{10}^{-3}}$s |

Here the unit kilogram is the SI unit not the gram. More smaller or larger units can be derived from one unit using prefixes. Note that the prefixes are used for the gram in case of mass not kilogram (I don't think you can add prefix to kilogram). Those prefixes represent the multiples of 10 or 1/10.