The language of Physics: Units and Measurements

Science and everyday life measure the world using units; these universal languages of science facilitate precision and accuracy in everything humans do. They also allow for exact testing, technological evolution, and multinational collaboration. In everything from engineering marvels to preparing food, and even navigating, standard units are the fundamental building blocks of comprehension and advancement. Without them, science would fail, commerce would flounder, and international communication would be hampered. They quantify the world, and as a universal language, they enable our combined efforts to meet our grand challenges and build a quality of life, thus serving as critical drivers in the realization of a more knowledge-based and interconnected society.

So, let's explore the world of units and measurements.

Quantity:

Anything we can measure is called a quantity. Yes, we can measure length, mass, current, temperature, and so on, but what about love, friendship, and pain? Of course, we can't measure them. So, the point is that anything we can measure is called a quantity.

Units:

Units are words or groups of symbols that represent quantities.

For example, we measure mass in kilograms (kg), so kg is the unit of mass.

There are two major types of units:

1. Fundamental Units:

Fundamental units are based on basic assumptions. There are only 7 basic assumption-based units, which are called Fundamental Units. All other units are derived from these 7 fundamental units.

   1. Kilogram: Unit of mass, symbol 'kg'.

   2. Meter: Unit of length, symbol 'm'.

   3. Second: Unit of time, symbol 's'.

   4. Ampere: Unit of current, symbol 'A'.

   5. Mole: Unit of amount of substance, symbol 'mol'.

   6. Candela: Unit of luminous intensity, symbol 'cd'.

   7. Kelvin: Unit of temperature, symbol 'K'.

2. Derived Units:

  All units except the 7 fundamental units are derived units because they are derived from these fundamental units.

Example:

Force has the derived unit "Newton." We measure force in Newtons. 

How is Newton derived from fundamental units?

Formula of Force:

   Force = m.a

   where 'm' represents mass and 'a' represents acceleration.

   So, force = kg.m/s²

   Here, kg is the fundamental unit used for mass, and m/s² has the fundamental units of meter and time.

Watch and Read More

Dimension:

A dimension is the representation of a physical quantity in terms of fundamental units such as length, mass, and time.

Example:

Dimension of Speed:

As we know,

Speed = distance/time

So,

LaTeX Formulas:

Dimension of Speed:

\[ \text{[Speed]} = \frac{\text{[Distance]}}{\text{[Time]}} = \frac{[L]}{[T]} = [L/T] \]

Formula of Force:

\[ \text{Force} = m \cdot a \]

where \( m \) represents mass and \( a \) represents acceleration.

\[ \text{Force} = \text{kg} \cdot \frac{\text{m}}{\text{s}^2} \]

 

Principle of Homogeneity:

In the Principle of Homogeneity (POH), we can easily find the dimension of an unknown in an equation. The equation must have terms with the same unit and dimension.

Application of Dimension:

Dimension is used for:

1. Checking whether an equation is dimensionally correct or incorrect.

2. Converting systems of units.

3. Deriving formulas dimensionally.