How Do You Calculate the Rotational Inertia of a Composite Object?

AI Thread Summary
To calculate the rotational inertia of the composite object consisting of a circular hoop and a square made of four thin bars, the relevant formulas for each component's inertia must be applied. The inertia of the hoop is calculated using I = mr^2, while the inertia of the rods is determined using I = 1/3 mr^2 for those perpendicular to the axis of rotation. The total rotational inertia is found by summing the individual inertias of the hoop and the rods. The user is struggling to combine these correctly, particularly with the orientation of the rods affecting their contribution. Accurate calculations are essential for determining the overall rotational inertia of the structure.
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Rotational Inertia Problem--PLEASE HELP!

Homework Statement



Figure 12-39 shows a rigid structure consisting of a circular hoop, of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis with a period of rotation of 1.0 s. Assuming R = 0.50 m and m = 3.0 kg, calculate the structure's rotational inertia about the axis of rotation

The figure is attached

Homework Equations



I of point mass = mr^2
I of hoop = mr^2 or .5mr^2
I of rod = 1/3 mr^2

The Attempt at a Solution



I tried to add the I of the hoop and two of the rods together (because the other two rods are parallel to the rotating axis) but nothing that I've tried really worked...
 

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