## Physical Quantity

*Physical Quantities are those which are measurable. Mass, length, time, speed, force, etc are some examples of physical quantities*. Here, the mass measure the quantity of matter, time measures the duration. Similarly, speed measures that how fast something moves.

There are two parts in a physical quantity, one is ‘**number**‘ and another is ‘**unit**‘. The number indicates “*how much*” the quantity is there. The unit helps us to identify the “*which physical quantity is this*“.

## Unit:

If you go to a grocery store and ask the shopkeeper to give potato, then the shopkeeper will definitely ask you a question – “*How much?*” If your answer is something like 5, then again “*what 5?*” So, basically just saying a number does not make any sense. To make it sensible or meaningful we need to put something after the number 5. So what we put after the number is called “**unit**“. Therefore you need to specify the unit (kilogram i.e. 5 Kg) so that people can understand the exact amount of physical quantity.

The unit helps us to know the exact amount of physical quantity.

The unit of a given physical quantity is unique.

The unit represents a standard quantity of that physical quantity. As an example, the length of a rod = 5 m (meter). This means 5 multiplied by 1 meter. So here length is a physical quantity, its numerical value is 5 and unit is m (meter). Here 1 m refers to a certain amount of predefined length. 5 m is 5 times this standard amount (1 m).

There are two types of units - 1. Fundamental unit 2. Derived unit.

**Fundamental Unit**: The units which are independent of other units are known as fundamental units.

**Length, mass, and time** – these are three base quantity and their units are base units or fundamental units (meter kilogram, second respectively).

**Derived Unit**: Derived units are derived from fundamental units.

Velocity, force, momentum, density, etc are derived quantity and their units are derived units (m/s N, Kg-m/s, Kg/cubic meter respectively).

## System of Unit:

There are three methods used around the world for a long time, these are –

**c.g.s**= centemeter-gram-second**M.K.S**= meter-kilogram-second**F.P.S**= foot-pound-second

## Some Physical Quantities and their Units

Physical Quantity | CGS | MKS | FPS |
---|---|---|---|

Length | centimeter (cm) | meter (m) | foot (ft) |

Mass | gram (g) | Kilogram (kg) | pound (Ib) |

Time | second (s) | second (s) | second (s) |

Area | cm^{2} | m^{2} | ft^{2} |

Volume | cm^{3} | m^{3} | ft^{3} |

Density | g/cm^{3} | Kg/m^{3} | Ib/ft^{3} |

Velocity | cm/s | m/s | ft/s |

Acceleration | cm/s^{2} | m/s^{2} | ft/s^{2} |

Force | dyne g. cm/s ^{2} | Newton (N) Kg. m/s ^{2} | poundal |

Pressure | dyne/ cm^{2} | N/ m^{2} | poundal/ ft^{2} |

Work Energy | erg dyne-cm | Jule (J) N.m | ft.poundal |

Power | erg/s | Jule/sec Watt (W) | ft.poundal/s |

## Si Unit (International system)

In order to measure the same physical quantity in a separate single method, a separate measuring instrument has to be made for each method. Apart from that, it is not possible to disclose the data obtained from various measurements in a consistent manner. So to remove this problem the International Bureau of Weights and Measures adopted a single approach internationally to address this problem. This is known as the SI system (Système international).

## Symbol of Units:

Symbols are used to abbreviate each unit. A tradition of how to write different symbols has been recognized internationally. There are some rules to write units.

- The dot marks can not be placed between or after the symbol. Example: centemeters: cm (not c.m)
- S or es cannot be added to denote plural. E.g 5 gram = 5 g (not 5 gs).
- The first letter of the unit symbol found in the names of the scientists will be capitalized, the other symbol will use only lower case. Example: force = 5 Newtons = 5 N. [ kelvin- K, Pascal -Pa, Celsius-° C].
- Units should follow the division and multiplication rules of algebra (cm ✖ cm = cm
^{2}). - The degree symbol (°) should not be used to express the unit of temparature in kalvin unit (should use only K).

## List of 7 Base Quantities and Units:

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

Length | Metre | m |

Mass | Kilogram | Kg |

Time | Second | s |

Electric Current | Ampere | A |

Temperature | Kelvin | K |

Amount of Substance | Mole | mol |

Luminous Intensity | Candela | cd |

The term “** unit less quantity**” refers to a condition in which no fundamental quantities are involved. It doesn’t have a unit, hence it doesn’t have any dimensions.

## Supplementary Units:

Supplementary units are dimensionless units. Angle (measured in radians) and solid angle (measured in steradian) are two supplementary units.