Spinning Pencil: Finding the Optimal Spin Speed for Upright Balance

[ehrenfest]

[SOLVED] spinning pencil

Homework Statement

A pencil is set spinning in an upright position. How fast must the spin be in order that the pencil will remain in the upright position? Assume that the pencil is a uniform cylinder with length a and diameter b. Find the value of the spin in revolutions per second.

Homework Equations

The Attempt at a Solution

I am so confused about this problem. If we are assuming "ideal" conditions, why would it not remain in an upright position no matter how slow you spin it? If everything is ideal, how could it possible tilt or fall or anything? If we are not assuming ideal conditions, what is not ideal? I believe that this question makes no sense.

 

[ehrenfest]

please?

 

[D H]

If the pencil is not spinning, any deviation from perfectly upright will make the pencil fall over. The perfectly upright position is a metastable equilibrium state if the pencil is not spinning. If the pencil is spinning very fast, the upright position is a stable equilibrium state. Find the rotation rate at which the equilibrium transitions from metastable to stable.