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    The centripetal force for uniform motion in a circle vari... — Carmelics
    Statements
    321,452
    Perspectives
    108,905
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    Home/Causation
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    The centripetal force for uniform motion in a circle varies as v²/r

    CausationTruth & Knowledge
    ?Rate how convincing each reason is below to see the overall strength.
    1 reason for
    2 reasons against

    Reasons For

    1 perspective
    Reason for
    ?
    • 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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    Reasons Against

    2 perspectives
    Reason against 1 of 2
    ?
    • 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 against 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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    Related

    Applying a theorem about fixed geometric figures to quantities defined only in a...Berkeley argued in 'The Analyst' (1734) that reasoning about nascent or evanesce...By Euclid's Elements Book 3 Proposition 36, PR² equals QR times twice the radius...Euclid's Elements Book 3 Proposition 36 applies strictly to static chord-secant ...
    +7 moreShow less
    If the limiting procedure is logically incoherent without the rigorous epsilon-d...In the limit as Q approaches P, PQ approaches PR, so t² equals PR²/v²Newton's limit argument assumes the geometric ratio QR/PR² converges to 1/2r, bu...Substituting these relations yields force ∝ v²/SP, i.e., v²/rThe force varies as QR/t²The substitution in P4 therefore smuggles in the very continuity and differentia...The time t is proportional to PQ divided by the velocity v

    Similar

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    Source

    AI-extracted1/3 agreementValid
    SEP: newton-principia
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    move from P to Q, and hence the force varies as QR/t2. But the time is proportional to PQ divided by the velocity v, and in the limit as Q approaches P, PQ approaches PR, so that t2 becomes equal to PR2/v2. Proposition 36 of Book 3 of Euclid entails that in this limit PR2 is equal to the product of QR and twice the radius SP, and hence the force for uniform motion in a circle varies as v2/SP or v2/r.[35]
    Extraction notes

    Validity: Extracted via Max plan + API grounding/validity checks

    Details

    Type
    claim
    Perspectives
    3 (1 for, 2 against)
    Edits
    1 edit