How to calculate the moment of inertia of a system with multiple bodies?

AI Thread Summary
To calculate the moment of inertia of a system with multiple bodies about the OO' axis, each body's moment of inertia must be determined individually using the relevant equations, particularly the parallel axis theorem. After calculating the moment of inertia for each body, the results should be summed to find the total moment of inertia for the system. It is essential to show the calculations for each body separately to validate the final answer. Providing detailed work will help others review and confirm the accuracy of the calculations. This method ensures a comprehensive understanding of the moment of inertia for the entire system.
CollinsArg
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Homework Statement


Calculate the moment of inertia in the OO' axis of the following figure (image attached).

Homework Equations


The relevant equations are in the image,
except: I = Icm + m.h2 (formula of moment of inertia to change the axis from the centre of mass to a parallel axis).

The Attempt at a Solution


I tried to find the moment of inertia of each figure separately/individually depending of the OO' axis by the formula give in "relevant equations" then sum all up to find the total moment of inertial of the system. Is this right? I'm not sure how to evidence this is correct
 

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You need to show more work before one can tell whether your answer is correct. Your method is correct. You have 5 bodies, you need to calculate the moment of inertia about axis OO' for each one separately then add all the results. If you want someone to check your work, please provide the 5 separate moments of inertia, not just the final answer.
 
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