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?

 

[pmacias]

I can understand your confusion about the purpose of squaring in equations, particularly in physics. Let me explain the reasoning behind squaring in equations and how it helps us understand and solve problems in physics.

Firstly, it's important to understand that squaring is a mathematical operation that involves multiplying a number by itself. For example, 5 squared (5^2) is equal to 5 x 5, which gives us 25. In physics, we use squaring to represent the relationship between different physical quantities, such as distance, time, and velocity. By squaring these quantities, we can better understand their relationship and how they affect each other in a given scenario.

In the example you mentioned, the equation T = 2 pi * square root(L/g) represents the relationship between the period (T) of a pendulum, the length of the pendulum (L), and the gravitational acceleration (g). By squaring the period (T), we are essentially representing the time it takes for one full swing of the pendulum. This squared value helps us to better understand the relationship between T, L, and g and how they affect each other in the equation.

Similarly, in the equation T2 * g / (4 pi) = L, the squared T represents the period squared, which helps us to understand the relationship between T, g, and L. It may seem counterintuitive to square a time value, but in physics, it is a common practice to use squared values to represent relationships between different physical quantities.

In essence, squaring in equations helps us to simplify and understand complex relationships between physical quantities. It allows us to see how these quantities are related to each other and how they affect each other in a given scenario. I hope this explanation helps to untangle your thinking about squaring in physics equations. Keep exploring and questioning, as that is what science is all about.