What is the sweet spot for rotational kinematics?

[Pogorz]

Homework Statement

i've altered this image to be easier to read. ignore problem 1 except for the information given. the picture of the rotating object is for problem 2, which is the problem i need help with
http://img32.imageshack.us/img32/3690/screenshot20091121at931x.th.png

2. The attempt at a solution

i've solved for 'w' when the rotating bar is vertical, as well as velocity tangential. my issue is the whole 'sweet spot' definition.

 

[Delphi51]

You must have d, L and x=L/2 in your answer for v.
Hopefully the expression can be arranged so these appear together as d/L.
You are just asked to replace each d/L with Z.

 

[Pogorz]

I've attempted to solve the problem, found the centre of mass to be Xcm = (L+2d)/3. Not sure where to go from there, though.

 

[Delphi51]

Use your expression for the linear speed of the tip.
Replace every d/L with z.