# SI Unit for Physical Quantities

## Base Unit

Physical quantities are aspects of the universe that we can measure. Some very easily, such as the distance across a lab, others more of a challenge like the distance to the nearest star. Both, however, are the same quantity, distance. They should be measured in the same units. In this case, meters, although we do use other units for very large or very small quantities. These, however, are based on the standard unit, known as the SI Unit.

The International System of Units, (SI units), is the standard set of units used for measurements in science. Having an agreed standard is very important, it means all scientists in all countries are measuring quantities in the same way.

**Base units of measurement**

These six represent quantities that are fundamental to physics. They are combined to make other units of measurement. The symbols used are either an abbreviation of the unit of measurement, such as kg for Kilogram, or they are named after famous scientists. Abbreviations are written in lower case and those named after people are in uppercase.

The SI unit for temperature is the kelvin, named after Lord William Kelvin so the symbol is ‘K’.

Quantity | SI Unit | Symbol |

Distance | meter | m |

Mass | Kilogram | kg |

Time | second | s |

Electrical Current | ampere | A |

Temperature | kelvin | K |

Mass of material | mole | mol |

This ammeter is used to measure the base unit of Electrical current in amperes (A)

There are some additions to these that are commonly accepted, but they are not strictly SI units. You will have used liter or millilitres to measure the volume of a liquid. This is acceptable, but in some situations, you will see cubic-meters (m^{3}) or cubic-centimeters (cm^{3}) used. The m^{3} is the SI unit of volume.

Celsius is often used to report temperatures, this is acceptable too, but the kelvin is the SI unit. These two are acceptable because the commonly used units match the magnitude of the SI unit. For example 1 ^{o}C = 1 ^{o}K.

## Derived Units

Derived units are used for quantities that are calculated from measurements of two or more base units.

The area of a square is a simple example. To measure area we take two measurements of distance and then multiply them together. We do the same with the units.

i.e. Area = length x breath (distance x distance)

so the units are

meter x meter (m x m) or square meter (m^{2})

Speed is another common example used in physics.

Speed = distance ÷ time

Speed = meters ÷ second

The units of speed are therefore; m/s. Which can also be written as ms^{-1}

All quantities that are not base units have an SI unit of measurement based on combining the base units. There are some exceptions, force is a good example.

Force = mass x acceleration, (mass in kg and acceleration is m/s/s) so the units of force can be written as; kg.m/s/s, (kilogram meter per second per second).The convention, however, is to use the newton, (N).

## Derived Units with Special Units

There are a number of quantities that use a unit of measurement that is not a derived unit using the base SI units. These are often named after famous scientists.

The SI unit for force is one very famous example. We use the unit a newton (N), named after Sir Isaac Newton.

Here are the others you will need for this course.

Quantity | Unit | Symbol | Named after |

Frequency | hertz | Hz | Heinrich Rudolf Hertz |

Force | newton | N | Sir Isaac Newton |

Energy | joule | J | James Prescott Joule |

Power | watt | W | James Watt |

Pressure | pascal | Pa | Blaise Pascal |

Electrical charge | coulomb | C | Charles Augustin de Coulomb |

Electrical potential difference | Volt | V | Alessandro Volta |

Electrical resistance | ohm | Ω | Georg Ohm |

Magnetic flux density | tesla | T | Nikola Tesla |

Note: You do not need to know the name of the scientist for the exam, only the quantity, the unit, and the symbol.

When writing these units, they should always be written in lowercase when using the full name, but the symbols are written with the first, or only letter as a capital.

- Why is it important for scientists to use SI units when measuring and reporting their findings?
- Your answer should include: same / standard

Explanation:*So that all scientists are using the same standard and everyone can understand the answers and compare them with their own results.* - What is a key difference between a base unit and a derived unit?
- Your answer should include: measured / measure / calculated / calculate

Explanation:*Base units must be measured, derived units can be calculated from measuring base units and combining them.*