# Free falling rotational motion

1. Dec 8, 2004

### 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?

Last edited: Dec 8, 2004
2. Dec 8, 2004

### Staff: Mentor

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...