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Angular velocity of a yo-yo!

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    A certain yo-yo can be modeled as a uniform cylindrical
    disk with mass M and radius R and a lightweight hub of
    radius ½R. A light string is wrapped around the hub.

    (a) First, the yo-yo is allowed to fall. Find the angular
    velocity of the yo-yo when the string has unwrapped a
    distance L.

    (b) Now, imagine that that you pull upward on the string such
    that the yo-yo remains in the same place. Find the angular
    velocity of the yo-yo when you have pulled the string
    upward a distance of L.

    (c) Explain in words why it makes sense that the answers to
    parts (a) and (b) are different.


    2. Relevant equations

    K (total) = .5 * I (center of mass) *w^2 + .5MR^2

    I cm for a uniform cylindrical hub = .5M(R^2 + (.5R)^2)

    3. The attempt at a solution

    (A)
    K (total) = .5 * I (center of mass) *w^2 + .5MR^2 = MgL

    W^2 = MgL/ (.5 *I (cm) + .5MR^2)

    I cm for a uniform cylindrical hub = .5M(R^2 + (.5R)^2)
    So..

    W^2 = MgL/(.5 * (.5M(R^2 + (.5R)^2) + .5MR^2)

    W^2 = MgL/(1/4Mr^2 + 1/16MR^2 + 1/2MR^2)

    W^2 = gL/(13/16R^2)

    Does that seem about right? (obviously need to make it the square root but just leaving it squared for now)

    (b)
    I assume I cannot use conservation of energy, so maybe I could solve this with the Work that is done? I dunno, I'm confused I guess I don't know where to begin

    Thanks for any help fellow physics buds!
     
  2. jcsd
  3. Mar 9, 2010 #2
    Just realized that I probably should have taken into account the Inertia of the lighweight middle area but that will just change the general format of the first problem. It's the second problem that remains confusing
     
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