Moment of Inertia + Energy question

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Homework Help Overview

The problem involves a uniform rod pivoted at one end, with a focus on calculating the angular speed as it moves from an inclined position to a horizontal position. The subject area includes concepts of rotational dynamics and energy conservation.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to calculate the moment of inertia and angular speed using energy conservation principles but questions the correct expression for height in the context of the pivot point.

Discussion Status

The discussion appears to be ongoing, with participants seeking clarification on the setup and parameters involved in the problem. There is no explicit consensus yet, and further exploration of the assumptions regarding height and pivot point is noted.

Contextual Notes

Participants are considering the implications of the pivot location on the moment of inertia and the height used in energy calculations. There is a hint provided regarding the moment of inertia, but the original poster expresses uncertainty about the correct application of the height in their calculations.

darkspym7
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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=[tex]\sqrt{\frac{6gh}{L^2}}}[/tex], 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
 
Last edited by a moderator:
Anyone?
 
I still don't know.
 

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