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    Carmelics

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    Made withinDC&Austin
    Statements
    321,452
    Perspectives
    108,905
    Topics
    42
    Home/Original/inverse
    See Original
    Inverse View

    It is not the case that The centripetal force for uniform motion in a circle varies as v²/r

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Newton's limit argument assumes the geometric ratio QR/PR² converges to 1/2r, but this convergence requires the curve to have a well-defined second-order osculating circle at P.
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    • 2.Berkeley argued in 'The Analyst' (1734) that reasoning about nascent or evanescent quantities involves a logical fallacy: quantities are treated as non-zero during calculation, then set to zero in the conclusion.
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    • 3.If the limiting procedure is logically incoherent without the rigorous epsilon-delta foundations unavailable to Newton, the derived ratio v²/r inherits that foundational illegitimacy.
      ?

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    Reason for 2 of 2
    ?
    • 1.Euclid's Elements Book 3 Proposition 36 applies strictly to static chord-secant relationships in a completed circle, not to dynamically evolving geometric quantities approaching a limit.
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    • 2.Applying a theorem about fixed geometric figures to quantities defined only in an idealized limiting process conflates the mathematics of actual circles with the mathematics of instantaneous curvature.
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    • 3.The substitution in P4 therefore smuggles in the very continuity and differentiability assumptions the argument was meant to establish geometrically.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.The force varies as QR/t²
      ?

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    • 2.The time t is proportional to PQ divided by the velocity v
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    • 3.In the limit as Q approaches P, PQ approaches PR, so t² equals PR²/v²
      ?

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    Explore the most compelling reason on the other side.