Understanding the Purpose of Squaring in Equations: A Question in Physics

[DmytriE]

Hi all,

I have been thinking long and hard and trying to rationalize the reason for squaring an equation. I still don't understand why we do it. It's mainly in physics that I don't get it. I understand full well and accept that to get the area of a circle you multiply pi by r^2. But why do you have to to square the r? Is it because you have to take into account both the length and width of the circle?

If this is true, then why do we square T in the following equation? What does a squared T (period) represent? The period can't represent length and width so then what does it?

T² * g / (4 pi) = L

The previous equation was rearranged from:

T = 2 pi * square root(L/g)

Any help trying to untangle my thinking would be great.

 

[Drakkith]

Well, pi is the ratio of the circumference to the diameter. In a square you would just square the diameter to find the area. However in a circle of equal diameter you have less area, so instead of squaring the diameter you square the radius and multiply times pi. I'm not really sure what you are looking for. A general answer is that it is simply the required mathematical operation or something like that.

 

[gsal]

Here, let me google that for you...here is the reasoning behind the formula for calculating the area of a circle: http://www.worsleyschool.net/science/files/circle/area.html"

And http://scienceblogs.com/builtonfacts/2010/01/period_of_a_pendulum.php" is the derivation for the period of a pendulum

 

[SteamKing]

Area of a circle = 2 pi r^2?