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Path Coordinates and constant circular acceleration.

  1. Sep 25, 2008 #1
    1. The problem statement, all variables and given/known data

    A top is made to spin by unwinding the string wrapped around it. The string has a length of 0.64m and is wound at a radius of 0.02m (neglect string thickness). The string is pulled such that top spins with a constant angular acceleration of 12 rad/s^2. Determine the velocity and acceleration vectors in path coordinates when the string has completely unwound. Assume that the top starts from rest.


    2. Relevant equations

    a=(tangential acceleration)*[tex]\hat{t}[/tex]+(normal acceleration)*[tex]\hat{n}[/tex]

    v=(magnitude of velocity vector)*[tex]\hat{t}[/tex]
    3. The attempt at a solution

    The string pulls so that 16[tex]\pi[/tex] revolutions occur which is approximately 315.8 radians.

    Tangential acceleration = r*[tex]\alpha[/tex] or (.02m)(12 rad/s^2) (or is this only for constant circular speed situations?)

    I am pretty well lost on this one. Where do I begin?
     
  2. jcsd
  3. Sep 25, 2008 #2

    LowlyPion

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    Homework Helper

    First are you sure that it's 16*π is the number of revolutions?

    As to figuring the velocity maybe you can use the usual kinematic equations?

    Vf2 = Vo2 + 2*a*x

    Only V is in radians/s and x is in radians?
     
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