Units & Calculations

• 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]
• Derived Units

  • 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
• Derived Units

  • 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