What is phi? Understanding Conservative Forces

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SUMMARY

The discussion centers on the concept of phi in the context of conservative forces, specifically defined by the equation \(\vec F(\vec r) = \phi(r') (\vec r)/r\). It is established that U, the potential energy, is represented as \(U(\vec r) = -\int_0^r \phi(r') dr'\). The participants conclude that phi represents the magnitude of the force vector, applicable primarily to central forces. The validity of the initial equation is challenged, indicating it does not hold for non-central forces.

PREREQUISITES
  • Understanding of vector calculus
  • Familiarity with conservative force fields
  • Knowledge of potential energy concepts
  • Basic principles of central forces in physics
NEXT STEPS
  • Study the mathematical derivation of conservative forces
  • Explore the implications of non-central forces in physics
  • Learn about the relationship between force and potential energy
  • Investigate applications of central force equations in orbital mechanics
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Physics students, educators, and professionals interested in classical mechanics, particularly those focusing on force fields and potential energy relationships.

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When you define \vec F(\vec r) = \phi(r') (\vec r)/r
Now U is usually denoted

U(\vec r) = -\int_0^r \phi(r') dr'

What is phi?
 
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It would appear that phi is just the magnitude of the Force vector...

EDIT: after looking at it a bit more, I don't believe the first equation can be true in general. Since the only vector on the RHS is the r vector, that means this equation would only work for central forces. In that case, phi should indeed be the magnitude of the force vector. If the forces are not central forces...then you can't get the equation to hold no matter what you set phi to.
 
Yeah they are central, thx.
 

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