What do we mean by Physics? Physics is an effort in observing, measuring and predicting the outcome of physical phenomenon that happen around us. For that we must quantify the physical quantities so we can study the relationship between them.
For ex. Suppose we measure the mass of an object as 5kg. Here ‘mass’ is the physical quantity and ‘kg’ is the unit.
Base units
Let us try to define a set of base units which can define the universe around us comprehensively.
To begin, let’s consider some common quantities you must have come across so far:
1) Length - SI unit: metre
2) Mass - SI unit: kilogram
3) Time - SI unit: second
These 3 are commonly measured physical quantities. We included them in our base set because they are independent of each other i.e. not one of them can be resolved or broken down further into the other 2.
What about Force? Force is the product of mass and acceleration. Acceleration is function of length and time. This means Force can be completely explained using mass, length and time. Which means it cannot be included in this base set.
Force = mass * a = mass * f(x, t) - not an independent quantity.
While force cannot be included in our base set, another base set consisting of Force, Length and Time is also valid. In this set Mass will be defined using Force, Length and Time.
There are other physical phenomena which introduce new physical quantities:
4) Current - SI unit: Ampere, Used in: Electricity and Magnetism
5) Temperature - SI unit: Kelvin, Used in: Thermal phenomenon
6) Mole - SI unit: mol, Used to measure quantity of matter
It is important to note here that this is different from mass. Mol denotes amount of matter while mass is a property of matter. Mass denotes gravitational mass. It represents the resistance of matter to force.
7) Luminous intensity - SI unit: candela, Used to measure intensity/brightness of light
Besides these 7 there are 2 other commonly used physical quantities. They are dimensionless ratios so we cannot include them in our base unit set. They are grouped as supplementary units.
1) Angle - radian
2) Soild angle - steradian
SI system
The SI system was published in 1960 and is now the most widely used system of measurement. It is built around the 7 base units we discussed earlier
S.I. - “le Système International d’unités”
Derived Quantities
Remember why we excluded Force from out base set? It was because we were able to describe it using quantities already in our set. Such quantities are called derived quantities.
Ex: Force, Energy, Coefficient of linear expansion
Like the variable physical quantities, universal physical constants also can or cannot have dimensions.
For ex. E = mC^2, C is the speed of light measured in m/s (constant)
α is fine structure constant, a dimensionless constant used in quantum field theory
Conversion of units
Same physical quantity can be represented by different units. For ex. We can say the length of a line segment is 2cm or 20mm or 0.02m and we will be correct in all cases. Obviously, different units of same physical quantity will have the same dimensional formula. Units can easily be converted into each other by calculating their ratios.
Dimensional Analysis
Any valid physical expression/equation must follow some basic rules:
1) In case of addition or subtraction both the quantities being added or subtracted must have the same dimensions (a, b).
For ex, if we add 2 quantities A + B
A and B must have same dimensions
2) Both the sides of an equation should have same dimensions.
For ex, if A = B
A and B must have same dimensions
3) A quantity in exponential power or logarithmic or trigonometry or inverse trigonometry functions must be dimensionless.
A = BC or A = Log C or A = Sin C or A = Sin-1 C
C must me dimensionless
These rules can be used in simple dimensional analysis
For ex. We can use this to verify dimensional integrity of a given equation.
Note here that a physically valid equation must be dimensionally correct but not every dimensionally correct equation will be true physically.
For ex. If A, B and C have same dimensions, then consider these 2 equations
A = B + C
A = B - C
While both equation are dimensionally correct, both cannot simultaneously be physically correct.
We can also use dimensional analysis to calculate unit of a physical quantity in a given equation
For ex. Q: Calculate the unit of gas constant R in given equation
PV = nRT
A: Here,
P: Pressure
V: Volume
N: Number of moles
T: Temperature
R: Universal gas constant.
R = PV/nT
Dim (R) = Dim (PV/nT) = (ML^-1T^-2 x L^3) / (Mol x K) = ML^2T^-2Mol^-1K^-1