Moment of Inertia of 4 Balls on Square Side

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Homework Help Overview

The problem involves calculating the moment of inertia for a system of four solid balls positioned at the corners of a square. Each ball has a specified mass and radius, and the moment of inertia is to be determined about one of the sides of the square.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of the parallel axis theorem and question how it is applied to the balls in the system. There is confusion regarding the inclusion of terms in the moment of inertia calculation, particularly the addition of certain components.

Discussion Status

The discussion is ongoing, with some participants clarifying their understanding of the moment of inertia calculation. One participant expresses gratitude for the clarification regarding the contribution of the two balls along the axis, indicating a productive exchange of ideas.

Contextual Notes

There appears to be some uncertainty about the application of the parallel axis theorem and the specific contributions of each ball to the overall moment of inertia. The original poster's calculations and the reasoning behind them are under scrutiny.

erisedk
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Homework Statement


There are four solid balls with their centres at the four corners of a square of side a. The mass of each sphere is m and radius is r. Find the moment of inertia of the system about one of the sides of the square.

Homework Equations

The Attempt at a Solution


I= 2 (two balls) × [ 2/5 mr^2 (Icm) + ma^2 ] (just used parallel axis theorem)

However, in the answer,
I = 2 ( 2/5 mr^2 ) + 2×[ 2/5 mr^2 + ma^2 ]

Why have they added 2 ( 2/5 mr^2 ) ??
 
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Using the parallel axis theorem is good. I don't see it under 2. What does it look like and for what balls do you apply it ?
 
erisedk said:
There are four solid balls

Why have they added 2 ( 2/5 mr^2 ) ??
Consider the above two lines.
 
Ok, right!
I got it, thanks. I didn't consider moi of the two balls along the axis.
 

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