# Fundamental and Derived quantities,units and dimensions

Physical quantities have no meaning, unless is measured quantified and give a unit. Therefore we need number or quantity and unit of measurement to specify physical quantities.

There two type of physical quantities, **Fundamental** and **derived quantities.**

Among the fundamental quantities we have three most important, there LENGTH, MASS, and TIME. The units of these three quantities form the base on which units of other quantities driver their units

**Other fundamental quantities are:**

Electric current

Temperatures

Luminous intensity

Amount of substances

Scientists all over the world try to use the same unity to measure the same quantity. Therefore the system of unit accepted all over the world is called SYSTEM INTERNATIONAL UNITS (SI UNITS).

**FUNDAMENTAL QUANTITIES AND UNITS**

QUANTITIES | UNITS |

LENGTH | METER (m) |

MASS | KILOGRAM (kg) |

TIME | SECOND (s) |

TEMPERATURE | KELVIN (k) |

ELECTRIC CURRENT | AMPERE (a) |

AMOUNT OF SUBSTANCE | MOLE (mol) |

LUMINOUS INTENSITY | CANDELA (cd) |

##### How to Measure length, mass and volume

Introduction to the study of physics

**Derived quantities and units**

Derived quantities and the units are obtained by combination of basic units . For example, unit of volume is obtained by multiplying the units of length three times. ie **m × m × m =m ^{3 }** which is pronounced as meter cubed or cubic meter. Density is the ratio of mass and volume , therefore the unit of density is

**kg/m**

^{3 }or kgm^{-3 }, which is pronounced kilogram per meter cubed, speed is defined as a distance divided by time so the unit is m/s or ms

^{-1}and is pronounced meter per second.

**See other derived units and their physical quantity below**

QUATITY | DERIVATION | UNIT |

Area | Length × breadth | M^{2} |

Volume | Length × breadth x height | M^{3} |

Density | Mass/volume | Kgm^{-3} |

Velocity | Displacement/time | Ms^{-1} |

Acceleration | change in velocity/time | Ms-^{2} |

Weight | Mass x acceleration due gravity | Newton (N) |

Momentum | Mass x velocity | Newton second (Ns) |

Pressure | Force/ area | Pascal or Nm^{-2} |

Energy or work | Force X distance | Joule (j) or Ns |

Power | Work/time | Watt (w) or js-^{1} Or NmS-^{1} |

# SUMMARY

Fundamental quantities are the basic quantities that are independent of the other quantities.

Fundamental unit are unit upon other units formed

Derived quantities and unit are those formed obtain by combination of fundamental quantities and units.

# DIMENSION** OF PHYSICAL QUANTITIES**

The dimension of physical quantity indicates how the SI unit is made up. That is expression of physical quantities in term of dimension of three fundamental units: Length(L) Mass(M) and Time(T)

For example the dimension of density:

Density= M/V= M/L^{3}= ML^{-3}

The dimension of acceleration:

Acc^{n} = V/t =S/t^{2}=LT-^{2}

The dimension of force F:

F=Ma=MLT-^{2 }

### **Other physical quantities, their units and dimension**

PYSICAL QUANTITIES | UNITS | DIMENSION |

Velocity | Ms-^{1} |
LT-^{1} |

Acceleration | Ms-^{2} |
LT-^{2} |

Force | N (ma) | MLT^{-2} |

Momentum | Kgms-^{1} |
MLT-^{1} |

Density | Kgm-^{3} |
ML-^{3} |

Pressure | Nm-^{2} |
ML-^{1}T-^{2} |

Young’s modulus | Nm-^{2} |
ML-^{1}t-^{2} |

Surface tension | Nm-^{1} |
MT^{-2} |

**Important of dimension**

Dimension can be used to determine or verify whether a physical equation is correct or not, as the dimension of both sides of the equation must be the same, for the equation to be correct.

For example

### S= ut =1/2at^{2}

Where s= distance

U= initial velocity

a=acceleration

t= time

The dimension of S = L therefore the other side of the equation most be L

Solution

Ut =s/t x t= s = L

1/2at^{2} = s/t^{2} x t^{2} = S= L

S= ut =1/2at^{2 }, but S =L, ut =L and 1/2at^{2 }=L

Therefore, the dimension of S= ut =1/2at^{2}

Is L =L, this shows that the equation is right dimensionally.

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