Moment of Inertia Calculation for Offset Mass

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Discussion Overview

The discussion revolves around calculating the moment of inertia for an offset weight configuration in a rotating system. Participants explore various methods for determining the moment of inertia, including the use of the parallel axis theorem, and address challenges related to the geometry of the system and the representation of calculations.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes a dilemma in calculating the moment of inertia for an offset weight configuration and requests assistance.
  • Another participant suggests calculating the moment of inertia for each mass individually and summing them, though they express confusion about the provided drawing.
  • A participant mentions the lack of a standard shape formula for the specific geometry involved, which includes a rectangular steel billet and a steel frame.
  • There is a discussion about deriving the distance to the rotating axis from the center of mass versus the center of gravity.
  • Some participants reference the parallel axis theorem as a method to find the moment of inertia about a different axis.
  • One participant expresses a desire for an example calculation to clarify the application of the parallel axis theorem.
  • Another participant emphasizes the importance of showing calculations step by step for verification purposes.
  • A participant identifies themselves as a professional engineer working on a patented project, indicating that their situation involves complex movements of multiple masses around a center point.
  • There is a suggestion that an approximation for moment of inertia can be used when the mass dimensions are significantly smaller than the radius arm length.
  • One participant notes that the movement of the masses as the system rotates complicates the calculation of moment of inertia.

Areas of Agreement / Disagreement

Participants express various viewpoints on how to approach the calculation of moment of inertia, with no consensus reached on a single method or solution. Disagreements arise regarding the interpretation of the drawing and the best approach to take for the calculations.

Contextual Notes

Participants mention limitations related to the representation of calculations on the forum and the challenges of using older technology for communication. There are also references to the need for accurate representations of the geometry involved in the calculations.

Pinon1977
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Ran into a bit of a dilemma. I'm having some problems calculating the moment of inertia for an offset weight configuration. Please see the attached drawing. Basically this offset weight will be turning around an axis as labeled in the drawing. Any help would be greatly appreciated
 

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Can't quite understand your drawing, but can you just find the moment of inertia for each mass individually and then add them up?
 
The drawing depicts a front view and side view of a tower that is rotating about an axis. To answer your question, yes; however I cannot find a standard shape formula for this geometry. The 50lbs is a rectangular steel billet and the frame is steel 3" flat bar.
 
Do you drive the distance to rotating axis value from the CL of my tower axis or from the center of mass?
 
Derive. Sorry not drive.
 
The table gives you the moment of inertia about a given shape's center of mass. Then you can use the parallel axis theorem to find its moment of inertia about your axis.
 
That's where in stuck. Can you provide me an example?
 
  • #10
So, for instance, the 50lbs that is 40in away fron the rotating axel would have a MOI of 23.41 kg.m2?
 
  • #11
?.??.?
 
  • #12
If you want someone to check your calculations, show what you did, step by step. (Do it symbolically as much as possible; call the mass m, and so on.)
 
  • #13
Yes I do want you to check my work, but u don't know how to put formulas on this message board. I'm using a very old smart phone and a lot if these newer features don't work on my phone. I just need to know if In the ballpark.
 
  • #14
So, I am politely suggesting that my question be transferred to someone who is a little more helpful and knowledgeable on the subject (as well as timely in their responses) Thanks Doc...
 
  • #15
Pinon1977 said:
So, I am politely suggesting that my question be transferred to someone who is a little more helpful and knowledgeable on the subject (as well as timely in their responses) Thanks Doc...
You won't find anyone more helpful or knowledgeable than Doc, you should be thankful he's been trying to help you. And we do not allow text speak on this forum it's YOU not U. Please spell out your words.

If you're trying to use an old phone that's incapable of doing what needs to be done, I suggest that you wait until you have access to a computer, all libraries have them if you do not have one.
 
Last edited:
  • #16
Pinon1977 said:
So, I am politely suggesting that my question be transferred to someone who is a little more helpful and knowledgeable on the subject (as well as timely in their responses) Thanks Doc...
Here's the deal:
(1) anyone who's willing to help you can jump in at any time. Good luck with that!
(2) the fact that you had to be told about the parallel axis theorem and a wiki page on moments of inertia indicates that you are a beginner -- nothing wrong with that! But don't expect someone to decipher your diagram or read your mind.

If you want help, show what you've done, step by step:
Pick an object. Describe its mass, dimensions, and rotational axis. (Use proper units.)
State the formula used to find its moment of inertia about its center of mass and your result.
Give the distance from the center of mass to the axis you really want. State how you applied the parallel axis theorem.

That way, should you have made an error somewhere we can point it out.
 
  • #18
I extend my apologies, sir. Here is my situation. I am a PE mechanical engineer that is working on a project (not a HS kid doing homework). Within the scope of this project is a machine that I've patented in which the animation of the machine involves 4 individual, multivarious "masses" moving in a non typical or unusual manner around a center point. I have yet to find a formula or equation that properly illustrates the MOI or kinetic energy of it's collective movements. I can certainly sketch it out for you, but I would rather not post this information on a public forum. Do you have an email I can send a SolidWorks Drawing to? Regards. John
 
  • #20
Evo said:
You won't find anyone more helpful or knowledgeable than Doc, you should be thankful he's been trying to help you. And we do not allow text speak on this forum it's YOU not U. Please spell out your words.

If you're trying to use an old phone that's incapable of doing what needs to be done, I suggest that you wait until you have access to a computer, all libraries have them if you do not have one.
Acknowledged, however, the "U" was a typo on my behalf (if you read the context in which it was used). The U and I are right next to one another on a keyboard.
 
  • #21
If the original diagram is anything like to scale then for anyone of the masses the approximation that Moment of Inertia = Mr2 where r is the length of the radius arm from mass CoG to axis of rotation can be used .

This approximation is commonly used and accurate within a few percent when the dimensions of the mass are significantly smaller than the length of the radius arm .

For a very accurate result under the same conditions break the mass into two or three sections each with a different radius arm and sum the individual Moment of Inertia contributions .
 
  • #22
It's not the mass itself that is troublesome, it's the movement of the mass as it's rotating. As the "tower" rotates 360 degrees continuously, there are two weights that move vertically inside the tower once it approaches the 12 o'clock position. It's within this movement that I would like to know the MOI changes.
 

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