QUADRATIC RELATIONSHIP IN PHYSICS

Quadratic relationships describe the relationship of two variables vary, directly or inversely, while one of the variables are squared. The word quadratic describes something of or relating to the second power. When it is a directly relationship will result to the shape of half of a parabola. In such a case, the two variables vary directly because they increase/decrease in conjunction. But they are described differently from a linear relationship because process of raising one of the variables to the second degree changes the rate of change every time.

[edit] Quadratic Relationships in Physics

Not all formulas in physics are linear; there are many that are quadratic as well. Just to name a few:

• Centripetal Acceleration: a_c = v²/r
  

• Kinetic Energy: KE = ½ mv²
  

• Law of Universal Gravitation:
  

Let’s explore with the Law of Universal Gravitation. In the equation, d is the distance between the centers of the masses and G is the universal constant—one that is the same everywhere. According to Newton’s equation, if the mass of a planet near the sun were doubled, the force of attraction would be doubled. Similarly, if the planet were near a star having twice the mass of the sun, the force between the two bodies would be twice as great. In addition, if the planet were distance from the sun, the gravitational force would be only one quarter stronger.

In this law, the distance varies inversely quadratic to the gravitational force and varies directly quadratic to G and the two masses.