Minimal angular velocity of a swinging homogenous stick ?

[CandiedPaper]

Homework Statement

Find the required angular velocity of the stick swinging around it's end axis (like a simple pendulum only without the added mass) at the point of "balance" (where the sinus function crosses the x-axis I suppose, sorry for the "weird" translation) so that it will be able to make one full rotation.

I am given it's length and it's "swing time" for small displacements (getting sin(θ) = θ using the Maclaurin series)

Homework Equations

The Attempt at a Solution

I have attempted it by setting the potential energy at the above position at full and kinetic at zero, but I am not given a mass for the stick, and I doubt my approach was very sane given the problem.

 

[barryj]

If you know the swing time, can you find the mass by using the formula for the period of a pendulum?

 

[voko]

Assume the mass is given. Work out the kinetic and potential energies of the stick. Then see if you really need the mass to solve the problem.