What is the relationship between the moment of inertia and the length of a rod?

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Homework Help Overview

The discussion revolves around the moment of inertia of a rod, specifically examining its relationship with the rod's dimensions, including length and diameter. Participants are exploring how these factors influence the moment of inertia when considering different axes of rotation.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants are attempting to clarify the moment of inertia for a rod with a specified diameter and length, questioning the assumptions made about its shape and the implications for calculations. There is discussion about the moment of inertia being zero along the length of the rod and the relevance of the rod's radius in determining its moment of inertia.

Discussion Status

The discussion is active, with participants providing various interpretations of the moment of inertia based on the rod's geometry. Some guidance has been offered regarding the formulas for calculating the moment of inertia about different axes, but there is no explicit consensus on the correct approach for the axis along the length of the rod.

Contextual Notes

Participants are navigating the complexities of the problem, including the distinction between treating the rod as a line versus a cylinder, and how this affects the moment of inertia calculations. There is an emphasis on the need to consider both the radius and length in the context of the problem.

merlos
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The moment of inertia about an axis along the length of a rod is zero, correct?
 
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merlos said:
The moment of inertia about an axis along the length of a rod is zero, correct?
Almost. If the rod has a measurable radius, it is a cylinder.
 
In all the other parts ot the problem though I considered it a rod.

Here's the problem:

Find the moment of inertia about each of the following axes for a rod that is 0.280 cm in diameter and 1.70 m long, with a mass of 5.00×10−2 kg.

A. About an axis perpendicular to the rod and passing through its center.
I = (1/12)ML^2
I = .012 kgm^2

B. About an axis perpendicular to the rod passing through one end.
I = (1/3)ML^2
I = .048 kgm^2

C. About an axis along the length of the rod.
 
merlos said:
In all the other parts ot the problem though I considered it a rod.

Here's the problem:

Find the moment of inertia about each of the following axes for a rod that is 0.280 cm in diameter and 1.70 m long, with a mass of 5.00×10−2 kg.

A. About an axis perpendicular to the rod and passing through its center.
I = (1/12)ML^2
I = .012 kgm^2

B. About an axis perpendicular to the rod passing through one end.
I = (1/3)ML^2
I = .048 kgm^2

C. About an axis along the length of the rod.
The rod has a diameter. It has a moment of inertia about the long axis.
 
So, I = (1/4)MR^2 + (1/3)ML^2 ?
 
The length of the stick--or cylinder--parallel to the axis doesn't matter, only the radius.
 

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