Moment of inertia (disk with off center hole)

AI Thread Summary
To calculate the moment of inertia (MoI) of a disk with an off-center circular hole, the MoI of the hole must be subtracted from that of the disk. The parallel axis theorem can be applied to account for the hole's offset from the center of mass. However, determining the mass of the hole is necessary, which can be calculated using the disk's mass and density derived from its area. This approach allows for accurate MoI calculations essential for further analysis of rotational dynamics. Understanding these principles is crucial for engineering applications involving rotating bodies.
Imperitor
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I have a disk with some thickness to it and I need its moment of inertia.
So this is the formula with r1=0
37f7b2c6aaaf32e1972af5e228064928.png


Now there is a "circular hole of diameter 'd' at a distance of 'r' from the geometric center of the disk." So I'm thinking that I should subtract the MoI of the hole from the disk. Here is a picture if you need it.

http://img99.imageshack.us/img99/782/50817033.jpg

I could use the same MoI equation as I did for the disk on the hole but that doesn't account for the hole being off centered. Any ideas??

I need to eventually equate this to a small mass rotating around a center point, so if there is a more direct approach please tell me. Thanks in advance for the help.
 
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Welcome to PF!

Hi Imperitor ! Welcome to PF! :smile:
Imperitor said:
I could use the same MoI equation as I did for the disk

That's right! :smile:

And then use the parallel axis theorem to find the moment of inertia about an axis not through the centre of mass. :wink:
 
Thanks. I really should have known that...

I'm really enjoying this forum. It's a great resource for an engineering student.
 
Wait a minute... hit another snag. To use that theorem I need to know what the mass of the missing hole is. I only know the mass of the disk as is (with the hole in it). Also the first formula I gave could only be used if I knew what the mass of the disk was with the hole filled in. This is driving me nuts. I can't even start working on the question I'm doing without getting this MoI.
 
just got up… :zzz:
Imperitor said:
Wait a minute... hit another snag. To use that theorem I need to know what the mass of the missing hole is. I only know the mass of the disk as is (with the hole in it). Also the first formula I gave could only be used if I knew what the mass of the disk was with the hole filled in. This is driving me nuts. I can't even start working on the question I'm doing without getting this MoI.

Easy-peasy …

divide the given mass by the area, to give you the density :wink: …

then multiply by each area separately! :smile:
 
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