Moment of Inertia of half disk

AI Thread Summary
The discussion focuses on calculating the mass moment of inertia for a half disk spinning around its center axis. The formula for a full disk is I=1/2*M*R^2, and it is clarified that the moment of inertia for the half disk is indeed half of this value due to the reduced mass. There is some initial confusion regarding the rotation not being through the center of gravity (COG), but it is confirmed that the same formula applies. The key takeaway is that the moment of inertia for the half disk simplifies to half that of the full disk because it has half the mass. This understanding helps in accurately determining the inertia for practical applications.
Brad123
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Hello, just found this forum didn't know it existed. hopefully someone can help with this.

I am trying to figure out the mass moment of inertia for a half disk spining around the center axis. A full disk is I=1/2*M*R^2. Would the inertia for spining a half disk around the center axis just be half of this? Not homework, something I am working on.

Hopefully someone here can help
 
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Brad123 said:
I am trying to figure out the mass moment of inertia for a half disk spining around the center axis. A full disk is I=1/2*M*R^2. Would the inertia for spining a half disk around the center axis just be half of this?
Yes.

Just to be clear: The formula will be the same, but since the mass is halved, the moment of inertia will be halved.
 
Thanks for the quick responce. What was confusing me was that the half disk is rotating around what is the center (not COG) I thought it might get more complicated due to the rotation not being through the COG. thanks just 1/2 the formula for a full disk because it is half the mass. Here is an image for reference. Apreciated. (I am ignoring the small attachment point for simplicity)
 

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