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Old Jun 15th 2014, 07:50 PM   #1
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Rotational Inertia about an offset axis

Problem gives 3 point masses all in the xy-plane. If I were asked to calculate the rotational inertia of the system about the z-axis, I would naturally use the magnitude of the position vector from each point to the origin where the closest distance to the z-axis is located. I can do it with vectors or magnitudes and get the same result for I total-system rotational inertia. But, some problems give and offset .. like (0,1) .. to the perpendicular axis through that point. I assume I can use the magnitudes from each point to (0,1) and those are the position vectors, or distances, I need for each point. But I never see that. Instead, I see a bunch of + and - signs that give very odd distances, and are certainly not equal to the magnitude of the distance from the point to (0,1). I have to assume that I simply do not understand what is meant by the offset point given. So what is really meant by that point ?

Here's an example of my thinking: point Q is at ( 4, 4 ) so the mag of the position vector is Sqrt( 4^2 + 4^2 ) ^2 which is 32. OK, if I'm given an offset point (1,0) for this calculation, now Q is sqrt( 3^2 + 4^2 )^2 and that is totally logical. But every example I see will give a ridiculous number for that distance from point Q to the offset point (1,0) through which the perpendicular axis is located. That makes no sense at all, unless there is some kind of offset jargon that I just don't understand.

Last edited by johns123; Jun 15th 2014 at 08:00 PM.
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Old Jun 16th 2014, 08:08 AM   #2
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Perhaps if you shared an example of the "bunch of + and - signs that give very odd distances" we could describe what it's doing. One suggestion - are you aware of the parallel axis theorem for calculating moment of inertia? If you know the moment of inertia I_cm for a system as measured about an axis through the system's center of mass, the moment of inertia as measured about an axis displaced distance 'r' from the center of mass is: I_cm + mr^2. So perhaps what they are doing is a calculation of the offset from the center of mass to the point of interest?
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Old Jun 16th 2014, 12:34 PM   #3
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Today, I was browsing through more Yahoo examples of the multi-point problems, and I found 1 that totally agreed with my idea of how to solve these problems .. even to an offset point. I found 4 or 5 that clearly did not use the magnitude of the position vector to the offset point. I think those solutions are in error because they simply are putting numbers in formulas without understanding the concept. The concept of rotational inertia in these problems is that the rotational inertia is a constant magnitude .. not a signed vector. They are confusing angular momentum concept with the scalar component of angular momentum. Yes, you can use vectors .. and dot product them together, but they are treating them as part of the cross product in the wrong formula. I'm using the Reese textbook, and he doesn't explain anything well .. plus he spread the rotation problems between chapters 4, 6, and 10 .. total confusion?
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