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.

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