Fundamental & Derived Units in Physics (DP IB Physics): Revision Note

SI units & prefixes

International system of units (SI)

• In science, there are 7 fundamental SI units which are used to measure various physical quantities 

Fundamental SI units table

• These base SI units form the foundation for measuring various properties and quantities in physics and other sciences

• Note: the candela is not used in IB Physics

Prefixes

• When dealing with powers of 10, we can use standard prefixes to denote the size of a quantity

• Some common examples include

  • kilowatts, kW (× 10³ W)

  • centimetres, cm (× 10^–2 m)

  • milligrams, mg (× 10^–3 g)

• The most common prefixes used in physics are listed in the table below

  • This list of prefixes can also be found in the data booklet

Table of common prefixes in physics

Symbols in physics

• There is a large number of symbols used in physics:

  • Mathematical symbols

    • e.g. Δ represents the change in a quantity

  • Fundamental constants - given in the data booklet

    • e.g. = the speed of light in a vacuum, = Planck's constant

  • Terms in physics equations - relevant equations are given in the data booklet

    • e.g. , where  is force,  is mass, and  is acceleration

  • Electrical circuit symbols - given in the data booklet

    • e.g. cell, resistor, voltmeter

  • Units and prefixes for quantities

    • e.g. specific heat capacity measured in J kg^–1 K^–1

  • Nuclear notation

    • e.g. where 12 is the nucleon number, 6 is the proton number, and C is the chemical symbol for carbon

    • Note: recall of chemical symbols is not required

Derived units

Express derived units in terms of SI units

• All units can be derived from the seven fundamental SI units

• These are known as derived units

• The fundamental unit of a quantity can be deduced from its definition

  • newton (N), the unit of force

    • force = mass × acceleration

    • N = kg × m s^–2 = kg m s^–2

  • joule (J), the unit of energy

    • energy = ½ × mass × velocity²

    • J = kg × (m s^–1)² = kg m² s^–2

  • pascal (Pa), the unit of pressure

    • pressure = force ÷ area

    • Pa = N ÷ m² = (kg m s^–2) ÷ m² = kg m^–1 s^–2

Table of common derived units in physics

Common unit conversions

• In some situations, it is more common and convenient to use non-SI units

  • radians (rad)

    • Equivalent to the angle made when the length of the arc is equal to the radius of the circle

    • 1 rad =

  • kilowatt-hour (kW h)

    • Equivalent to the amount of electrical energy transferred by a 1 kW device in 1 hour

    • 1 kW h = 3.60 × 10⁶ J

  • electronvolt (eV)

    • Equivalent to the amount of energy transferred when an electron is accelerated by a potential difference of 1 V

    • 1 eV = 1.6 × 10^–19 J

  • eV c^–2

    • Used to express the masses of atomic particles according to mass-energy equivalence

    • e.g. electron rest mass = 0.511 MeV c^–2

  • light year (ly)

    • The distance travelled by light in one year

    • 1 ly = 9.46 × 10¹⁵ m

  • parsec (pc)

    • The distance to a star that has a parallax angle of one arc-second

    • 1 pc = 3.26 ly

  • astronomical unit (AU)

    • The distance between the Earth and the Sun

    • 1 AU = 1.50 × 10¹¹ m

  • h, day, year

    • Units of time

    • 1 h = 60 × 60 = 3600 s

    • 1 day = 3600 × 24 = 8.64 × 10⁴ s

    • 1 year = 3600 × 24 × 365 = 3.15 × 10⁷ s