Physical quantities and SI units

Definition

Physical quantity

A physical quantity is a property of an object or system that can be measured, and is written as a number together with a unit.

Definition

SI unit

An SI unit is the internationally agreed unit used to measure a physical quantity, such as the metre, kilogram or second.

SI stands for the International System of Units, which gives scientists a common measurement language.
A complete measurement needs both a number and a unit, so $12$ is incomplete but $N12\ \text{N}$ states a force.
Base units are defined independently, while derived units are formed by multiplying or dividing other units according to an equation.
At GCSE, the most important SI base units are the metre $m\text{m}$ , kilogram $kg\text{kg}$ , second $s\text{s}$ , ampere $A\text{A}$ and kelvin $K\text{K}$ .

Units for motion and waves

Length, distance, displacement, height, extension and wavelength use the metre, $m\text{m}$ .
Area uses square metres, $m2\text{m}^{2}$ , because two lengths are multiplied.
Volume uses cubic metres, $m3\text{m}^{3}$ , because three lengths are multiplied.
Mass uses the kilogram, $kg\text{kg}$ , and must not be confused with weight.
Time and wave period use the second, $s\text{s}$ .
Speed and velocity use metres per second, $m/s\text{m/s}$ .
Acceleration uses metres per second squared, $m/s2\text{m/s}^{2}$ .
Density uses kilograms per cubic metre, $kg/m3\text{kg/m}^{3}$ .
Frequency uses the hertz, $Hz\text{Hz}$ , where $s−11\ \text{Hz}=1\ \text{s}^{-1}$ .
Angles use degrees, $∘^{\circ}$ .

Units for forces and energy

Force, weight, upthrust and resultant force use the newton, $N\text{N}$ .
Gravitational field strength uses newtons per kilogram, $N/kg\text{N/kg}$ .
Spring constant uses newtons per metre, $N/m\text{N/m}$ .
Energy transferred and work done use the joule, $J\text{J}$ .
Power uses the watt, $W\text{W}$ , with $J/s1\ \text{W}=1\ \text{J/s}$ .
Moment of a force uses the newton metre, $m\text{N m}$ .
Pressure uses the pascal, $Pa\text{Pa}$ , where $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Momentum uses kilogram metres per second, $m/s\text{kg m/s}$ .

Units for electricity and radiation

Electric current uses the ampere, $A\text{A}$ .
Potential difference uses the volt, $V\text{V}$ , where $J/C1\ \text{V}=1\ \text{J/C}$ .
Resistance uses the ohm, $Ω\Omega$ .
Electric charge uses the coulomb, $C\text{C}$ .
Magnetic flux density uses the tesla, $T\text{T}$ .
Radioactive activity uses the becquerel, $Bq\text{Bq}$ , where $Bq1\ \text{Bq}$ means one nuclear decay per second.

Units for thermal physics

Temperature uses degrees Celsius, $∘C^{\circ}\text{C}$ , or kelvin, $K\text{K}$ , according to the equation and data.
Specific heat capacity uses joules per kilogram per degree Celsius, $∘C)\text{J/(kg}\,^{\circ}\text{C)}$ .
Specific latent heat uses joules per kilogram, $J/kg\text{J/kg}$ .
Efficiency has no unit because it is a ratio of two quantities with the same unit, and it may be written as a decimal or percentage.

Example

A spring has force $NF=12\ \text{N}$ and extension $mx=0.080\ \text{m}$ , with $F = k x$ .
Rearrange the equation to $k=Fxk=\dfrac{F}{x}$ .
Substitute to give $mk=\dfrac{12\ \text{N}}{0.080\ \text{m}}$ .
Evaluate to obtain $N/mk=150\ \text{N/m}$ , because newtons are divided by metres.

Writing units accurately

Unit symbols named after people use capital letters, including $N\text{N}$ , $J\text{J}$ , $W\text{W}$ , $A\text{A}$ , $V\text{V}$ , $Hz\text{Hz}$ , $Pa\text{Pa}$ , $C\text{C}$ , $T\text{T}$ and $Bq\text{Bq}$ .
Written unit names use lower-case letters, including newton, joule and watt.
Unit symbols do not take a plural ending, so five newtons is written $N5\ \text{N}$ .

Common Mistake

Do not give mass in newtons or weight in kilograms, because mass and weight are different physical quantities.
Do not interchange energy in joules with power in watts.
Do not confuse a moment in $m\text{N m}$ with momentum in $m/s\text{kg m/s}$ .
Do not omit squared or cubed powers from $m2\text{m}^{2}$ , $m3\text{m}^{3}$ , $m/s2\text{m/s}^{2}$ or $kg/m3\text{kg/m}^{3}$ .

Exam technique

Write the requested unit beside every final numerical answer unless the answer line already supplies it.
Use the resulting unit to check the equation, because an acceleration result in $m/s\text{m/s}$ shows that the calculation is incomplete or incorrect.
Keep the unit visible during substitution when it helps distinguish quantities such as mass, weight, energy and power.

Self review

What two parts make a complete measurement?
Which units measure force, energy and power?
How can a derived unit be reconstructed from an equation?
Why does efficiency have no unit?

Physical quantities and SI units

Definition

Physical quantity

A physical quantity is a property of an object or system that can be measured, and is written as a number together with a unit.

Definition

SI unit

An SI unit is the internationally agreed unit used to measure a physical quantity, such as the metre, kilogram or second.

SI stands for the International System of Units, which gives scientists a common measurement language.
A complete measurement needs both a number and a unit, so $12$ is incomplete but $N12\ \text{N}$ states a force.
Base units are defined independently, while derived units are formed by multiplying or dividing other units according to an equation.
At GCSE, the most important SI base units are the metre $m\text{m}$ , kilogram $kg\text{kg}$ , second $s\text{s}$ , ampere $A\text{A}$ and kelvin $K\text{K}$ .

Units for motion and waves

Length, distance, displacement, height, extension and wavelength use the metre, $m\text{m}$ .
Area uses square metres, $m2\text{m}^{2}$ , because two lengths are multiplied.
Volume uses cubic metres, $m3\text{m}^{3}$ , because three lengths are multiplied.
Mass uses the kilogram, $kg\text{kg}$ , and must not be confused with weight.
Time and wave period use the second, $s\text{s}$ .
Speed and velocity use metres per second, $m/s\text{m/s}$ .
Acceleration uses metres per second squared, $m/s2\text{m/s}^{2}$ .
Density uses kilograms per cubic metre, $kg/m3\text{kg/m}^{3}$ .
Frequency uses the hertz, $Hz\text{Hz}$ , where $s−11\ \text{Hz}=1\ \text{s}^{-1}$ .
Angles use degrees, $∘^{\circ}$ .

Units for forces and energy

Force, weight, upthrust and resultant force use the newton, $N\text{N}$ .
Gravitational field strength uses newtons per kilogram, $N/kg\text{N/kg}$ .
Spring constant uses newtons per metre, $N/m\text{N/m}$ .
Energy transferred and work done use the joule, $J\text{J}$ .
Power uses the watt, $W\text{W}$ , with $J/s1\ \text{W}=1\ \text{J/s}$ .
Moment of a force uses the newton metre, $m\text{N m}$ .
Pressure uses the pascal, $Pa\text{Pa}$ , where $N/m21\ \text{Pa}=1\ \text{N/m}^{2}$ .
Momentum uses kilogram metres per second, $m/s\text{kg m/s}$ .

Units for electricity and radiation

Electric current uses the ampere, $A\text{A}$ .
Potential difference uses the volt, $V\text{V}$ , where $J/C1\ \text{V}=1\ \text{J/C}$ .
Resistance uses the ohm, $Ω\Omega$ .
Electric charge uses the coulomb, $C\text{C}$ .
Magnetic flux density uses the tesla, $T\text{T}$ .
Radioactive activity uses the becquerel, $Bq\text{Bq}$ , where $Bq1\ \text{Bq}$ means one nuclear decay per second.

Units for thermal physics

Temperature uses degrees Celsius, $∘C^{\circ}\text{C}$ , or kelvin, $K\text{K}$ , according to the equation and data.
Specific heat capacity uses joules per kilogram per degree Celsius, $∘C)\text{J/(kg}\,^{\circ}\text{C)}$ .
Specific latent heat uses joules per kilogram, $J/kg\text{J/kg}$ .
Efficiency has no unit because it is a ratio of two quantities with the same unit, and it may be written as a decimal or percentage.

Example

A spring has force $NF=12\ \text{N}$ and extension $mx=0.080\ \text{m}$ , with $F = k x$ .
Rearrange the equation to $k=Fxk=\dfrac{F}{x}$ .
Substitute to give $mk=\dfrac{12\ \text{N}}{0.080\ \text{m}}$ .
Evaluate to obtain $N/mk=150\ \text{N/m}$ , because newtons are divided by metres.

Writing units accurately

Unit symbols named after people use capital letters, including $N\text{N}$ , $J\text{J}$ , $W\text{W}$ , $A\text{A}$ , $V\text{V}$ , $Hz\text{Hz}$ , $Pa\text{Pa}$ , $C\text{C}$ , $T\text{T}$ and $Bq\text{Bq}$ .
Written unit names use lower-case letters, including newton, joule and watt.
Unit symbols do not take a plural ending, so five newtons is written $N5\ \text{N}$ .

Common Mistake

Do not give mass in newtons or weight in kilograms, because mass and weight are different physical quantities.
Do not interchange energy in joules with power in watts.
Do not confuse a moment in $m\text{N m}$ with momentum in $m/s\text{kg m/s}$ .
Do not omit squared or cubed powers from $m2\text{m}^{2}$ , $m3\text{m}^{3}$ , $m/s2\text{m/s}^{2}$ or $kg/m3\text{kg/m}^{3}$ .

Exam technique

Write the requested unit beside every final numerical answer unless the answer line already supplies it.
Use the resulting unit to check the equation, because an acceleration result in $m/s\text{m/s}$ shows that the calculation is incomplete or incorrect.
Keep the unit visible during substitution when it helps distinguish quantities such as mass, weight, energy and power.

Self review

What two parts make a complete measurement?
Which units measure force, energy and power?
How can a derived unit be reconstructed from an equation?
Why does efficiency have no unit?

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

Review 1.1.1 SI units for physical quantities by teaching Genie

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

Review 1.1.1 SI units for physical quantities by teaching Genie

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

Review 1.1.1 SI units for physical quantities by teaching Genie

1.1.1 SI units for physical quantities Revision Guide

1.1.1 SI units for physical quantities

Physical quantities and SI units

Units for motion and waves

Units for forces and energy

Units for electricity and radiation

Units for thermal physics

Writing units accurately

Review 1.1.1 SI units for physical quantities by teaching Genie

1.1.1 SI units for physical quantities Revision Guide