Are Energy Laws in Physics Really Just Coincidences?

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SUMMARY

The discussion centers on the similarities between various energy equations in physics, specifically highlighting the kinetic energy formula \(\frac{1}{2}mv^{2}\), the spring potential energy \(\frac{1}{2}kx^{2}\), rotational energy \(\frac{1}{2}I\omega^{2}\), and energy stored in capacitors and inductors. The participant questions whether these similarities indicate a deeper physical interpretation or are merely coincidental. They also note a derivational connection between rotational energy and kinetic energy, suggesting a mathematical consistency across different forms of energy.

PREREQUISITES
  • Understanding of classical mechanics, including kinetic and potential energy.
  • Familiarity with rotational dynamics and the moment of inertia.
  • Basic knowledge of electrical energy storage in capacitors and inductors.
  • Mathematical proficiency in manipulating algebraic expressions and units.
NEXT STEPS
  • Research the derivation of the rotational energy formula \(\frac{1}{2}I\omega^{2}\) from kinetic energy principles.
  • Explore the concept of energy conservation across different physical systems.
  • Investigate the role of dimensional analysis in establishing the similarity of energy equations.
  • Examine the implications of energy equivalence in various branches of physics.
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Students and professionals in physics, engineers working with mechanical systems, and anyone interested in the fundamental principles of energy across different physical contexts.

MHD93
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Hello

I've been wondering a lot of why many laws of energy in different branches of Physics seem similar, for example:

Kinetic:
<br /> \frac{1}{2}mv^{2}
Spring:
<br /> \frac{1}{2}kx^{2}
Rotational:
<br /> \frac{1}{2}I\omega^{2}
Capacitor:
<br /> \frac{1}{2}VC^{2}
Capacitor:
<br /> \frac{1}{2}eE^{2}
Magnetic:
<br /> \frac{1}{2}LI^{2}

Does this have a real physical interpretation, or is it is just by accident?
 
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A question I have been wondering about too.

Not too important here but, I believe (1/2)Iw^2 was derived using (1/2)mv^2, so that connects two of them.
 
If the units are the same the math has to be similar.
 

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