# Spinning Pencil (think top) Urgent help wanted

1. Feb 27, 2007

### ^_^physicist

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: $$S^2*(I_s)^2 > (4mglI)$$
is the only relavent equation I can think of. Where $$I_s$$ = 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