Physical Quantities And Units

Physical Quantities

These are the properties of a body which can be measured, for example, position, mass, charge, temperature, etc

Physical Quantities are expressed as a number plus and unit. A number on its own has no meaning - what is faster, a centimeter per second or furlong per fortnight?

SI Units

Physical Quantities are expressed as a number plus a unit. The preferred units are the SI Units

SI Unit Prefixes

The following prefixes are commonly used:

Prefix Magnitude Symbol
atto 10-18 a
femto 10-15 f
pico 10-12 p
nano 10-9 n
micro 10-6 μ
milli 10-3 m
centi 10-2 c
deci 10-1 d
deca 10 da
hecto 102 h
kilo 103 k
mega 106 M
giga 109 G
tera 1012 T
peta 1015 P
exa 1018 E

SI Base Units

The SI base units are as follows:

Quantity Unit Symbol
Mass kilogram kg
Time second s
Length meter m
Electric Current Ampere A
Thermodynamic Temperature Kelvin K
Amount of Substance mole mol
Luminous Intensity Candela cal

SI Base Unit Definitions

Note that the below definitions have been updated. These have only been included as they were the correct definitions of the SI base units at the time the book that is being followed in compiling these note was published. See Up-to-date SI Unit definitions

Quantity Unit Definition
Mass kilogram Mass of the International Prototype Kilogram
Time second The duration of 9192631770 periods of the radiation corresponding to the transition between to hyperfine levels of the ground state of a caesium-133 atom
Length meter The distance light travels in a vacuum in 1/299792458 seconds
Electric Current ampere The constant current which, if maintained in two straight parallel conductors of infinite length and negligible cross sectional area when placed one meter apart in a vacuum would produce a force of 2e10-7 newtons per meter of length between the two conductors
Thermodynamic Temperature kelvin The fraction 1/273.16 of the thermodynamic triple point of water
Amount of Substance mol The amount of substance of a system which contains as many elementary entities as there are atoms in 0,0012 kilograms of carbon-12

It can be seen from the above that their definitions have interdependency - they can only be defined in a particular order

Derived Units

The base units above can be combined to create derived units for all measurable physical quantities

Derived units can always be expressed in terms of both base units and base quantities.

Newtons are equivalent to kgms-2 and [M L T-2], where M = mass, L = length and T = time