Free falling rotational motion

[vabamyyr]

There is a post with length L and it is being cut down from its lowest point. So the post starts a free fall with circular trajector. The question is that what is the v of upper part of post when it hits the ground?

I used energetic method and mvL= 0,5mv^2 plus or minus something...
i have a feeling that it might be mgL= \frac 1 2 mv^2 - \frac 1 2 mgL \Longrightarrow v=\sqrt{3gL}

but i don't know how to prove it? Can anyone help me?

 

[Doc Al]

It's just conservation of mechanical energy, treating the falling post as being in pure rotation about the lowest point:
\Delta {PE} = - \Delta {KE}
mg\Delta h_{cm} = - 1/2 I \omega^2
... etc...