[Physics] Moment of inertia of a yo-yo

homework-and-exercisesrotational-dynamics

Considering the yo-yo like two CDs with a hollow cylinder between them, what is the moment of inertia of that object?

The axis that I must choose can't pass through the CM and be parallel to rotational axis that passes through the center of mass. A force $\vec{T}$ is pulling the object.

I can't use the Steiner theorem here, right? All because that cylinder cannot be ignored.

Another try that I do is calculating the moment of inertia of the three (well, two) objects and sum, but I think that this isn't correct.

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Best Answer

Use Steiner theorem and ignore the cilinder between the two disc.