Dimensions

The word "dimension" has a special meaning in physics it usually denotes the physical nature of a quantity.
Remember MLT as the symbol for mass, length and time respectively.

Just see the samples below to understand fully what dimension really means...




sample 1.
The formula for calculating the speed or velocity of a body is

thus the dimension of velocity is    
     

  =          

sample 2.
The formula for calculating the acceleration of a body is

           the dimension of acceleration is 

=       

but recall that " v " is not a fundamental quantity so we break it down further to derive its fundamentals,

sample 1 proved that the fundamentals of velocity is

therefore the true dimension of acceleration is

sample 3.
The formula for calculating force is

force(f) = mass(M) x acceleration(a)

the dimension of force is

f = M x a

recall that " a " (acceleration) is not a fundamental quantity, so we break it down to derive its fundamentals.

sample 2 proved that the fundamentals of acceleration

        the  true  dimension  of  force     f  =  M  x  

  

sample 4.
The formula for calculating the work done by a body is

work(e) = force(f) x distance(L)

note:in physics, distance and length are thesame...

the dimension of work is

e = f x L

" f " (force) is not a fundamental quantity so we break it down to derive its fundamentals,

sample 3 proved that the fundamentals of force    

  

    the dimension of work      e        x      L



                                                   =  



Assignment 1:
Derive the dimension for Area(A) if the formula is

length x width

Assignment 2:
Derive the dimension for pressure(P) if the formula is