Moment of Inertia/Torque about point O of the rod

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The moment of inertia of a thin rod about point O, located at a distance L/3 from one end, is calculated using the formula Irod = 1/3ML². To determine the torque due to the rod's weight when displaced by an angle θ, the gravitational force acting at the center of mass must be considered. For small angular displacements, the period of oscillation can be derived using the principles of rotational dynamics and simple harmonic motion. The discussion emphasizes the application of the Parallel Axis Theorem to find the moment of inertia about point O. Understanding these concepts is crucial for solving the problem effectively.
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Homework Statement


A thin rod of length L and mass M is free to rotate at a point O at a distance L/3 from one end.

a.) What is the moment of inertia of the rod about O?
b.) What is the magnitude of the torque due to the rod's own weight about O when it is displaced from the vertical by and angle θ?
c.) For small angular displacement, find the period of oscillation of this rod.

Homework Equations


Irod= 1/3ML2

The Attempt at a Solution


Not really sure what to do here
 
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First, what is the moment of inertia of a rod about its center? Then look up "Parallel Axis Theorem".
 

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