What is the sweet spot for rotational kinematics?

AI Thread Summary
The discussion focuses on solving a problem related to rotational kinematics, specifically determining the 'sweet spot' for a rotating bar. The user has successfully calculated the angular velocity and tangential velocity but is struggling with incorporating the variables d, L, and x into the final expression. They have found the center of mass to be Xcm = (L+2d)/3 and are seeking guidance on how to express the linear speed of the tip in terms of the variable z, defined as d/L. The goal is to rearrange the expression to include z appropriately. Clarification on these steps is needed to complete the solution.
Pogorz
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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.
 
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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.
 
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.
 
Use your expression for the linear speed of the tip.
Replace every d/L with z.
 

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