Why Do Phys Equations Use Squared Signs?

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SUMMARY

The discussion centers on the significance of squared terms in physics equations, specifically in formulas such as Centripetal Acceleration (v²/r) and Coulomb's Law (q₁q₂/d²). It is established that these squared terms arise from empirical observations, such as the inverse square relationship between force and distance in electrostatics. The squared distance in Coulomb's Law represents the surface area of a sphere centered at the charge, while in Centripetal Acceleration, it indicates the directional nature of velocity. Understanding these relationships is crucial for grasping how physical laws are formulated based on experimental data.

PREREQUISITES
  • Understanding of basic physics concepts, including force and acceleration.
  • Familiarity with Coulomb's Law and its applications in electrostatics.
  • Knowledge of kinematics, particularly the concepts of velocity and acceleration.
  • Basic mathematical skills, particularly in manipulating equations involving squares.
NEXT STEPS
  • Research the derivation of Coulomb's Law and its implications in electrostatics.
  • Study the concept of inverse square laws in physics, including gravitational and electromagnetic forces.
  • Explore kinematic equations, focusing on the role of velocity squared in calculating kinetic energy.
  • Investigate the geometric interpretation of physical laws, particularly how area and volume relate to force interactions.
USEFUL FOR

This discussion is beneficial for physics students, educators, and anyone interested in understanding the mathematical foundations of physical laws, particularly in the fields of mechanics and electrostatics.

majormuss
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Hi guys,
I have a question : why do some equations in Physics have a square sign. For example in the Centripetal Acceleration formula v(squared)/radius, Coulombs law, q(1)q(2)/distance(squared).
Can u explain it in a way that helps me understand the way formulae are discovered .
 
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Initially it was just discovered experimentally - for example, if you take two charged objects and you measure force between them, then you move them apart so that distance doubles - force gets four times smaller. You move them further, so that distance triples - and force goes down to one nineth of the original. That means force scales with the reciprocal of distance squared.
 
Hi.
Each square has proper meaning or interprtation, e.g.
Coulombs law, q(1)q(2)/distance(squared).: distance(squared) means surface area of the sphere centered at the charge.
the Centripetal Acceleration formula v(squared)/radius : positive, so centripetal for any direction of v. Kinetic energy 1/2 m v^2 is another example.

Regards.
 

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