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Physical quantities and units:

All physical quantities consist of a numerical magnitude and a unit and can be expressed in terms of the SI base units:

The base units are:

Derived units:

All units can be derived from products of the base units – it’s just simple algebra:

Text Box: Make sure you are comfortable with both ways of showing squared, cubed, square root etc … Eg:       Force in Newtons – express this in base units:

            F=  ma = kg  x  m/s2 

            Newton = kilogramme metre per second squared 

            Often shown as:  kgm/s2     OR   kgms-2   

Q1:      Derive the following into correct base units:

a)  speed   b)  acceleration  c)  pressure   d)  kinetic energy   e)  potential energy    f)  voltage  g)  resistance  h)  friction

Q2:      Prove by deriving into correct base units that the following equations are dimensionally correct:

a)      Energy = mass x speed of light squared

b)      Acceleration due to gravity = Weight in Newtons

           (in ms-2 )                    Mass in kilogrammes

Powers of ten

Very big and very small numbers can be shown like this

Take a careful note between the capital letters and the lower case  – it makes a difference – ask if uncertain

·          pico (p) 10-12

·          nano (n) 10-9

·         micro (m)10-6

·         milli  (m)10-3

·         centi (c) 10-2

·         deci (d) 10-1

·         kilo (k) 103

·         mega (M) 106

·         giga (G) 109

·         tera (T) 1012

Eg: 1 km = 1 x 103m = 1000metres

Q3:  Write the following out in full:

a)  10kJ   b)  2.56kV  c)  10cm  d)  100 mg  e)  5 MJ   f)  1.234 TW  g)  4.56 nK  h) 12 pHz 

Q4:  convert the following to the nearest power of ten symbol:

a) 10000m   b) 0.00004 A   c)  1.2 x 107 C