Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?