Why Is My Calculation of the Wheel's Moment of Inertia Incorrect?

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Homework Help Overview

The discussion revolves around calculating the moment of inertia of a wheel with respect to attached rods, specifically addressing the contributions from both the wheel and the rods. Participants are analyzing the application of the Steiner rule and the correct formulas for moment of inertia.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to apply the Steiner rule and combines the moments of inertia of the wheel and rods but questions their calculations. Some participants suggest revisiting the formulas used and clarify the counting of components in the total moment of inertia.

Discussion Status

Participants are actively engaging in clarifying the formulas and assumptions used in the calculations. There is a recognition of potential errors in the original poster's approach, particularly regarding the counting of the wheel and rods in the final expression. Multiple interpretations of the correct formula are being explored.

Contextual Notes

There is mention of a picture attached to the original post, which may provide additional context for the problem setup. The discussion also highlights the importance of correctly applying the moment of inertia formulas and the implications of counting components accurately.

dannee
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Homework Statement




i've attched a picture of the wheel, which need to calculate moment of intertia with respect to 8 rods.

i've tried to use stiener rule but it's not getting the answer,

moment of wheel is (m1*r^2)/2
moment of rod is (m2*r^2/3)

i use the rule i total = icm + mr^2

so it's 8*( (m1*r^2)/2 + (m2*r^2)/3 )

what am i missing?



Homework Equations



m1 = mass of wheel
m2 = mass of rod
r = length of rod

The Attempt at a Solution

 

Attachments

  • wheel.JPG
    wheel.JPG
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dannee said:
moment of wheel is (m1*r^2)/2
Revisit this formula.

so it's 8*( (m1*r^2)/2 + (m2*r^2)/3 )
There are 8 spokes but only 1 wheel.
 
that's right, 8 * 3(m2*r^2), i refer the moment of wheel is (m1*r^2)/2 and sum them,

but the correct answer is (3m2/8 + m1) * r^2
 
dannee said:
that's right, 8 * 3(m2*r^2), i refer the moment of wheel is (m1*r^2)/2 and sum them,
(1) Your formula for the moment of inertia of the wheel portion is incorrect.
(2) In your final result in post #1 you multiplied all terms by 8, thus counting the wheel 8 times.

but the correct answer is (3m2/8 + m1) * r^2
Double check that answer; looks like a typo.
 

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