Moment of Inertia + Energy question

AI Thread Summary
The discussion revolves around calculating the angular speed of a uniform rod pivoted at one end after being released from a 66° angle. The moment of inertia is calculated using the formula I = M(L/2)² + 1/12ML², and the potential energy is expressed as U = mgh. The challenge lies in determining the correct height (h) for the gravitational potential energy, with two possible interpretations: h = L*sin(theta) or h = (3/2L)*sin(theta). The user is seeking clarification on which height to use to accurately compute the angular speed when the rod is horizontal. The conversation highlights the importance of understanding the pivot point's effect on the height calculation in rotational motion problems.
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Homework Statement


A uniform rod of mass 3 kg is 17 m long. The rod is pivoted about a horizontal, frictionless pin at the end of a thin extension (of negligible mass) a distance 17 m from the center of mass of the rod. Initially the rod makes an angle of 66◦ with the horizontal. The rod is released from rest at an angle of 66◦ with the horizontal, as shown in the figure below The acceleration of gravity is 9.8 m/s2.
Hint: The moment of inertia of the rod about its center-of-mass is Icm = 1/12mL^2.

What is the angular speed of the rod at the instant the rod is in a horizontal position?
Answer in units of rad/s.


Homework Equations


U=mgh
K=1/2Iw^2


The Attempt at a Solution


The moment of inertia I got for the whole system was:
I=M(L/2)^2+1/12ML^2
I've managed to get:
w=\sqrt{\frac{6gh}{L^2}}}, with w being the angular speed
But I am unsure if h is L*sin(theta) or (3/2L)*sin(theta), since the rod is off the pivot.

Any ideas?
 
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Here's the figure that went along with it:

http://img103.imageshack.us/img103/9987/hw10q1ex1.jpg
 
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Anyone?
 
I still don't know.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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