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I can't figure out the moment of inertia for this motion. That is what I need help with.

I should be able to calculate the time period once I have found out the moment of inertia. How can I go about finding it?

My primary problem with finding the MOI is that while I try to calculate the MOI about the IAOR, the IAOR seemingly keeps changing (I believe the point of contact at any moment with the ground is the IAOR) Which is why I seem unable to calculate the MOI for the general motion.

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Daipayan Mukherjee,

Here's a hint for you: Start off by considering a complete, solid cylinder and then use the Parallel Axis Theorem. Do not hesitate if you need anymore help.

EDIT:

The diagram below might help you. You must first us the parallel axis theorem to relate it to the center of mass; and then use it a second time to point of contact C. While the point of contact varies with time, your exercise tells you that it is slightly tilted so I believe that this small change in distance is negligible when calculating the period of motion.

Moment of Inertia Half Cylinder

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  • $\begingroup$ Indeed.I understand that being symmetrically cut off, the half-cylinder will have the half the MOI about the initial cylinder axis as the full cylinder. I realise that then I would need to use the parallel/perpendicular axis theorem. But, to WHICH point do I translate my axis? The IAOR? But then where would the IAOR be? The point of contact of the hemi-cylinder with the ground?But that keeps changing,right? $\endgroup$
    – Daipayan Mukherjee
    Commented May 13, 2017 at 10:42
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    $\begingroup$ Please do not answer homework questions $\endgroup$
    – John Rennie
    Commented May 13, 2017 at 10:54
  • $\begingroup$ Daipayan Mukherjee, I have provided an edit of my answer. I believe it should be enough to guide you through your problem on finding the moment of inertia. $\endgroup$
    – Laudicina Corentin
    Commented May 13, 2017 at 11:00

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