Moment of Inertia/Torque about point O of the rod

In summary, the conversation discusses a thin rod of length L and mass M that is free to rotate at a point O. The moment of inertia of the rod about O is 1/3ML2 and the magnitude of the torque due to its own weight is discussed in relation to displacement and angle θ. The conversation also mentions the period of oscillation for small angular displacement and suggests looking up the Parallel Axis Theorem.
  • #1
Tygolfs94
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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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  • #2
First, what is the moment of inertia of a rod about its center? Then look up "Parallel Axis Theorem".
 

Related to Moment of Inertia/Torque about point O of the rod

1. What is moment of inertia?

Moment of inertia is a physical property of a rigid body that determines its resistance to changes in rotational motion. It is a measure of how mass is distributed around an axis of rotation.

2. How is moment of inertia calculated?

The moment of inertia of a rigid body can be calculated by multiplying the mass of the body by the square of its distance from the axis of rotation.

3. What is torque about point O of the rod?

Torque about point O of a rod is the measure of the force that causes the rod to rotate about point O. It is calculated by multiplying the force applied to the rod by the perpendicular distance between the point of rotation and the line of action of the force.

4. How is torque about point O of the rod related to moment of inertia?

Torque about point O of the rod can be related to moment of inertia through the equation τ = Iα, where τ is the torque, I is the moment of inertia, and α is the angular acceleration.

5. What factors affect the moment of inertia of a rigid body?

The moment of inertia of a rigid body is affected by its mass, shape, and distribution of mass around the axis of rotation. Objects with more mass and mass distributed farther from the axis of rotation will have a higher moment of inertia.

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