Units & Calculations (OCR GCSE Physics A (Gateway))

Units & Calculations

• There are a seemingly endless number of units in Physics

  • These can all be reduced to seven base units from which every other unit can be derived

• These seven units are referred to as the SI Base Units; this is the only system of measurement that is officially used in almost every country around the world

SI Base Quantities Table

• The seventh SI base unit is the candela (cd) which is the unit for luminosity 

  • This is not encountered at GCSE

Derived Units

• The seven SI base units are then used to derive other common units

• The base units of physical quantities such as:

  • Newtons, N [kg m / s²]

  • Joules, J [N m]

  • Pascals, Pa [kg / m s²]

• To deduce the base units, it is necessary to use the definition of the quantity

• The Newton (N), the unit of force, is defined by the equation:

  • Force = mass × acceleration

  • N = kg × m s^–2 = kg m s^–2

  • Therefore, the Newton (N) in SI base units is kg m s^–2

• The Joule (J), the unit of energy, is defined by the equation:

  • Energy = ½ × mass × velocity²

  • J = kg × (m s^–1)² = kg m² s^–2

  • Therefore, the Joule (J) in SI base units is kg m² s^–2

• The Pascal (Pa), the unit of pressure, is defined by the equation:

  • Pressure = force ÷ area

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

  • Therefore, the Pascal (Pa) in SI base units is kg m^–1 s^–2

Common Units Table

Prefix Notation

• Physical quantities can span a huge range of values

• For example, the diameter of an atom is about 10^–10 m (0.0000000001 m), whereas the width of a galaxy may be about 10²¹ m (1,000,000,000,000,000,000,000 m)

  • This is a difference of 31 powers of ten

• Powers of ten are numbers that can be achieved by multiplying 10 times itself

• These come under two categories of units:

  • Multiples eg. 10², 10³

  • Sub-multiples eg. 10⁻¹, 10⁻²

• Each power of ten is defined by a prefix, these are listed in the table below:

Prefixes Table

• Example conversions:

  • 12 GPa = 12 gigapascals = 12 × 10⁹ Pa (12 000 000 000 Pa)

  • 5 kN = 5 kilonewtons = 5 × 10³ N (5000 N)

  • 0.1 μA = 0.1 microamps = 1 × 10^–7 A (0.0000001 A)

  • 7 nC = 7 nanocoulombs = 7 × 10^–9 C (0.000000007 C)

Unit Conversions

• As well as prefix (powers of ten) conversions (eg. km into m) there are also common unit conversions

Time Conversions

• One such unit conversion are those for time

  • The main time conversions are shown in the table below:

Time Conversions Table

• A common time unit conversion is between hours and seconds

  • 1 hour = 60 minutes

  • 1 minute = 60 seconds

• Therefore 1 hour = 60 × 60 = 3600 seconds

  • To convert from hours → seconds, multiply by 3600

  • To convert from seconds → hours, divide by 3600

Hours × 3600 = Seconds

Temperature Conversions

• Another common temperature unit conversion is between Kelvin and degrees Celsius (ºC)

• The scale is defined as: 0 K = −273.15 ºC

  • To convert from Kelvin → Celsius, subtract 273

  • To convert from Celsius → Kelvin, add 273

 K − 273 = ^oC

  ^oC + 273 = K