2.1.3 Homogeneity of Physical Equations & Powers of Ten

• In Physics, every quantity has an appropriate unit
  • It is important that the correct unit is applied to that quantity

Table of Units

• A unit to the power of –1 (^–1) means ‘per’ eg. per metre = m^–1
  • If this is to the power of –2 or above, this means 'per' quantity squared eg. per unit area = m^–2

• Units of constants will be given on the data sheet
• There are a few cases when values have no units, these are:
  • When the value is calculated from a trigonometric function eg. cos(ωt)
  • Ratios, where both quantities have the same units eg. v / c
  • A number of something eg. number of molecules

• An important skill is to be able to check the homogeneity of physical equations using the SI base units
• The units on either side of the equation should be the same
• To check the homogeneity of physical equations:
  • Check the units on both sides of an equation
  • Determine if they are equal
  • If they do not match, the equation will need to be adjusted

How to check the homogeneity of physical equations

• 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
• It is useful to know the prefixes for certain powers of ten

          Powers of Ten Table