PROPORTIONALITY

The word 'proportional' appears in almost all the physics laws. Let us have a look at it.

Look at the above figures. Here, as the diameter increases, so is the circumference of the circles.

So circumference is proportional to the diameter. or
C is proportional 2r
hence, there must be some relationship between C and 2r. Or 2r is scaled to circumference by some number. That number is called constant of proportionality,

Therefore C= constant* 2r
or Constant= C/2r

By drawing numbers of circles, measuring C and Diameter and dividing one by the other, we can arrive at the constant which happens to be 3.14...=pi

Finally,C = pi*2r
C= 2*pi*r

other examples,
1. force is proportional to the momentum : constant=1
2. current is proportional to the voltage: constant=R. resistance of the wire.
Also
1. Frequency of the waves is inversely proportional to its wavelength.
Constant: Velocity of waves.
2. volume of gas is inversely proportional to the pressure
Constant =1

Nature loves proportionality. Our body structure must be proportional. Banana trees cannot bear coconuts.

A dot like LED produce powerful tiny light waves. But, to produce energetic sound waves, heavy speakers are required.

Comments

THE EARTH, A SUPER ORGANISM

JOIN MY COURSE: "Become a programmer in a day with python" A man called 'love lock' (what a name) proposed a theory called Gaia theory, named after Greek Goddess. It says, "Earth is a self-regulating organism like a human being. The organic life in it interacts with in-organic matter and maintains atmosphere, temperature and environment". Hence the earth is still suitable for the life to thrive. Imagine, in a particular place, there are lot of flowers. Some flowers are white and some are darkly coloured. We know, white reflects light and heat while dark absorbs the same. White flowers can thrive in hot climate. But dark flowers requires cold climate. The absorption and reflection balances and the environment reaches average, warm temperature at which both the flowers can co-exist. This is the essence of "Gaia" theory. On our earth, ...

DISORDER IS THE "ORDER OF THE DAY"

Imagine a balloon full of air. The air molecules are moving randomly inside the balloon. Let us pierce the balloon with a pin. The air rushes out. Why should not the air molecules stay inside the balloon safely and ignore the little hole? That is not the way the world works. The molecules always "want to occupy as many states as possible". Hence the air goes out in the open to occupy more volume. The things always goes into disorder (entropy) and the disorder increases with time. The above statement is what we call "second law of thermodynamics". Consider a cup of coffee on the table. Suppose the heat from entire room flows to your cup of coffee, the coffee will boil and the rest of the room will freeze. Freezing means bringing things to order and arrangement. It violates the second law. Hence it will never happen. Hence heat must flow from high ...

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pa...

sciencecapsules

Search This Blog