Relativistic centripetal force

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Discussion Overview

The discussion revolves around the concept of relativistic centripetal force, particularly in the context of a mass moving in circular motion at relativistic speeds. Participants explore the implications of relativistic effects on the calculation of centripetal force and the interpretation of measurements from different frames of reference.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant derived a formula for relativistic centripetal force but noted a lack of references in literature to corroborate this result.
  • Another participant sought clarification on the definition of "relativistic centripetal force," questioning whether it involved different time frames (lab time vs. proper time).
  • A hypothetical scenario was proposed involving Superman spinning a ball at relativistic speeds, prompting questions about the centripetal force experienced by the ball.
  • Concerns were raised about the frame of reference for measuring force, emphasizing that force is relative to the observer's frame.
  • Discussion included the potential variability of tension measured by a sensor depending on its position along the wire, suggesting that this could affect the readings of centripetal force.
  • One participant suggested calculating the 4-acceleration of the ball and provided a mathematical approach to derive it, including the use of geometric units.
  • There was a debate regarding the dimensional analysis of acceleration and whether the derived formulas were correct, with some participants questioning the interpretation of units used in the calculations.
  • Another participant defended the use of geometric units, arguing that they are commonly accepted in the context of special relativity, while others expressed skepticism about the implications of varying tension along the wire.

Areas of Agreement / Disagreement

Participants expressed differing views on the validity of the derived formulas and the implications of relativistic effects on measurements. There is no consensus on the correctness of the calculations or the interpretation of the results, indicating ongoing debate and uncertainty.

Contextual Notes

Limitations include potential misunderstandings of the definitions of terms like proper time and the implications of using geometric units. The discussion also highlights the complexity of measuring forces in relativistic contexts and the need for careful consideration of frame dependence.

  • #31
Rotation?

HallsofIvy said:
Do you remember that relativistic effect happen along the direction of motion?

What relativistic effect are you referring to?
 
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  • #32
malawi_glenn said:
the constant is 0.3*B, where B is measured in T, and p in GeV/c

Where is my suggested typo?

That forumula is widely used in particle physics.
Sorry, I misunderstood the question. It seems to me that you have two separate questions, though, if I'm understanding it correctly this time.

1) How do you compute the momentum of a particle, given its observed radius of curvature in a magnetic field of known strength. (You've supplied your own answer to this one, it looks right though I haven't double checked it)

2) What is the force (i.e. dp/dt) on that particle in the lab frame?

The answer gamma m v^2 / r is correct here as well with these assumptions.

Note that you have to specify a frame in order to ask what the 3-force is. One of the advantages of 4-forces is that they are geometric, frame-independent objects , but the magnitude of the 3-force definitely depends on the frame in which it is measured.
 
  • #33
pervect said:
Sorry, I misunderstood the question. It seems to me that you have two separate questions, though, if I'm understanding it correctly this time.

1) How do you compute the momentum of a particle, given its observed radius of curvature in a magnetic field of known strength. (You've supplied your own answer to this one, it looks right though I haven't double checked it)

2) What is the force (i.e. dp/dt) on that particle in the lab frame?

The answer gamma m v^2 / r is correct here as well with these assumptions.

Note that you have to specify a frame in order to ask what the 3-force is. One of the advantages of 4-forces is that they are geometric, frame-independent objects , but the magnitude of the 3-force definitely depends on the frame in which it is measured.

The thing is that I don't have a question, I just wanted to add what I obtained to this discussion.

Maybe I should have written "I WAS trying to derive this forumula.." And then I played a bit, and also searched in some books etc to werify my steps, that's all. And I wanted to contribute with my "research" in this thread, where to OP seemed to find the expression i posted.
 
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