# Free falling rotational motion

vabamyyr
There is a post with lenght 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 dont know how to prove it? Can anyone help me?

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$$\Delta {PE} = - \Delta {KE}$$
$$mg\Delta h_{cm} = - 1/2 I \omega^2$$