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Spinning Pencil (think top) Urgent help wanted

  1. Feb 27, 2007 #1
    1. The problem statement, all variables and given/known data
    A pencil is set spinning in an upright position. How fast must the spin be for the pencil to remain in the upright position? Assume that the pencil is a uniform cylinder of length a and diameter b. Find the value of the spin in revolutions per second for a=20cm and b=1cm. Express results in revolutions per second


    2. Relevant equations
    Assuming that this is a top problem: [tex] S^2*(I_s)^2 > (4mglI) [/tex]
    is the only relavent equation I can think of. Where [tex] I_s [/tex] = moment of inertia about the symmetry axis, and I= moment about the axes normal to the symmetry axis.


    3. The attempt at a solution
    Taking the above equation for the necessary speed for "sleeping" to occur (that is maintaining a the vertical), I mainpulate the equation into

    S > [(4*m*g*l*I)/(I_s)^2)]^(1/2). Now noting that this is a cylinder I come up with I_s=m*(a^2)/2 and I= m*(a^2/4+b^2/12); however, when I plug these values into the express I am not getting what the back of the book is getting, in fact if I plug in numbers I am off by a signifigant amount (3 orders of magnatute). So, from what I can tell I am making a mistake somewhere on figuring out the I and I_s values.

    The back of the book gives the equation as

    S > [ (128*g*a)/(b^4)*(a^2/3+b^2/16) ]^(1/2) = (when values are inserted as indicated in the question) 2910 RPS.

    Any ideas on how to figure out I and I_s
     
    Last edited: Feb 27, 2007
  2. jcsd
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