DIMENSIONS
Hello guys, lets talk about dimensions, students complaining of dimensions to me, so i decided to make a post and video on it. Now what is dimensions?
Dimensions is a concept of analysis which shows a relationship between fundamental and derived Quantities.
If you haven't watched my video on deriving fundamental quantities and units, you can watch it below
Dimensions also represents all physical quantities in terms of basic quantities; and the three basic quantities commonly used are:
1. Mass - M
2. Length - L
3. Time - T.
So we try to break down the physical quantity to Mass, Length and Time. Lets solve some examples.
1. Find the dimensions of velocity.
Solution.
velocity = displacement/time =m/s
metre is the unit of Length (L)
second is the unit of time(T)
substituting we have;
velocity = L/T =LT¯¹
So that's the dimensions of velocity.
2. Find the dimensions of acceleration.
Solution
Acceleration = velocity/time
velocity = displacement/time =m/s
Acceleration = velocity ×1/time= m/s×1/s=m/s².
Substituting we have
L/T².
3. Find the dimensions of Force.
Solution
Force = mass×acceleration
we know mass is in kilograms.
Acceleration from previous example is m/s² or ms¯²
Force=Kg×ms¯² =Kgms¯².
Kg is the unit of mass(M)
m is the unit of length (L)
s is the unit of time (T)
substituting we have
Force=MLT¯²
4. Find the dimensions of Workdone.
Solution
Workdone=Force×distance
Force is Kgms¯² from above
Workdone= Kgms¯² × s
Workdone = Kgm²s¯²=ML²T¯².
5. Find the dimensions of Momentum.
Solution
Momentum = mass × velocity
velocity is ms¯¹,mass is Kg
Momentum = Kg×ms¯¹=Kgms¯¹
MLT¯¹.
You can try to find the dimensions of :
1. power
2. Impulse
3. Energy
4. Pressure
5. Density.
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