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.
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.