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Homework Help: Helix (spool and wire) geometry

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data
    (From Stewart's Calculus Early Transcendentals (4th ed), Ch. 13 Problems Plus #8)

    A cable has radius r and length L and is wound around a spool with radius R without overlapping. What is the shortest length along the spool that is covered by the cable?

    2. Relevant equations

    See image link below.

    3. The attempt at a solution
    I've read the solution from the solutions guide and it makes sense, aside from this geometric representation:
    (h=vertical distance between coils)


    I'm trying to understand the rationale for this geometric image. Specifically, where is the 2Pi(R+r) coming from? This is clearly the circumference of the spool/cable, but I don't understand its presence in the image. Could someone describe what the image is showing (where the spool is, how it's oriented, what the two parallel line are, etc)? Thanks!

    Last edited by a moderator: Apr 24, 2017
  2. jcsd
  3. May 4, 2009 #2
    I thought I would repost the image, as the link above has too many ads.
    Any ideas?

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