Moment of Inertia of Rod w/ Masses M, m1, & m2

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Homework Help Overview

The problem involves calculating the moment of inertia of a rod with a specified mass distribution, including two additional masses positioned at defined distances from an axis of rotation. The context is centered around the application of the parallel axis theorem and the summation of moments of inertia.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the parallel axis theorem but expresses uncertainty about its application. Participants question the provided information, particularly regarding the axis of rotation and the orientation of the rod.

Discussion Status

The discussion is progressing with participants clarifying the setup of the problem. Some guidance has been offered regarding the need to sum the moments of inertia and the implications of the rod's uniform density. There is an exploration of how to express distances in terms of the rod's length.

Contextual Notes

There is a lack of explicit information regarding the center of mass and the specific distances of the masses relative to the axis of rotation, which participants are addressing. The original poster has noted that the axis of rotation is at the middle of the rod.

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Homework Statement


Find the moment of inertia of a rod with mass M, that has a mass m1, L/2 to the left of the axis of rotation and a mass m2, L/4 to the right of the axis of rotation. L is the length of the entire rod?

Not sure what to do. My professor said that I had to use the parallel axis theorem, but I am having trouble appling it to this problem, any help would be great!


Homework Equations



I = Icm + mr^2

The Attempt at a Solution

 
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You're not providing enough information, like where the axis of rotation is relative to the center of mass of the rod and how the rod is oriented.
 
Oh sorry about that. Well the rod is horizontal and I wasn't given the centre of mass. But the axis of rotation is at the middle of the rod.
 
If the rod is of uniform density, its center of mass will be in the middle, and the axis of rotation passes through this point.

From how you've described the problem, you don't need to use the parallel-axis theorem. You just need to sum the moments of inertia of the rod and the two masses.
 
oh ok so then the moment of inertia would just be

I = Icm +m1r1^2 +m2r2^2
 
Yup, you just need to find Icm in terms of the mass and length of the rod and express r1 and r2 in terms of L.
 

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