Is My Calculation of Moment of Inertia Using the Parallel Axis Theorem Correct?

AI Thread Summary
The calculation of the moment of inertia using the parallel axis theorem was confirmed as correct by participants in the discussion. It was suggested to maintain variables M and L until arriving at a single expression for the moment of inertia, which is 3.2ML². An alternative method was proposed, involving using the parallel axis theorem in reverse by finding the moment of inertia about the central mass and subtracting the product of the displacement squared. This approach simplifies the calculation process. Overall, the discussion provided validation and alternative strategies for calculating moment of inertia.
Romain Nzebele
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Homework Statement
If M=0.50Kg, L=1.2 m, and the mass of each connecting rod shown is negligible, what is the moment of inertia about an axis perpendicular to the paper through the center of mass? Treat the mass as particles.
Relevant Equations
Xcm=total mx/ total m
The picture of the problem and my attempt to solve it are below. Please let me know if my resolution is correct. Thank you in advance.
242976
1557069337351.png
 
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Yes, it looks right. Personally, I would have kept ##M## and ##L## until you had a single expression for the MoI. In this case ##3.2ML^2##.
 
PeroK said:
Yes, it looks right. Personally, I would have kept ##M## and ##L## until you had a single expression for the MoI. In this case ##3.2ML^2##.
Great, thank you so very much.
 
A slightly easier way is to use the parallel axis theorem 'in reverse'.
Find the MoI about the central mass M and subtract (Σm)x2, where x is the displacement to the common mass centre.
 

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