Center of Mass and Inertia Tensor Experimentation

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Discussion Overview

The discussion revolves around designing an experiment to determine the center of mass and inertia tensor of a small, non-symmetrical object. Participants explore various methods and equipment, including static and dynamic balancing techniques, to achieve these measurements.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • One participant suggests using gyroscopes and accelerometers for experimentation but seeks additional methods from others.
  • Another participant mentions that static balancing can determine moments of inertia, while dynamic balancing is necessary for products of inertia.
  • A participant shares their experience with a static balancing experiment but expresses difficulty in creating a dynamic balancing project to find the inertia tensor, citing a lack of understanding of the underlying theory.
  • One participant proposes a method for finding the center of mass by hanging the object from three points and drawing lines to find the intersection.
  • Concerns are raised about the stiffness of the wires used in the balancing experiment and its potential impact on results.
  • Questions are posed regarding how to calculate the off-diagonal components of the inertia tensor, with one participant indicating uncertainty about the procedure.

Areas of Agreement / Disagreement

Participants express a range of methods and ideas, but there is no consensus on the best approach for dynamic balancing or the calculation of the inertia tensor's off-diagonal components. Multiple competing views and uncertainties remain throughout the discussion.

Contextual Notes

Participants acknowledge limitations in their understanding of the theory behind inertia tensor calculations and the potential influence of experimental setup factors, such as wire stiffness.

landong
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Hello All,

I am trying to create an experiment to determine the center of mass and inertia tensor of an aribtrary object. This object is small (softball size), and non symmetrical on all axis. I have some thoughts concerning gyroscopes and accelorameters, but am curious to see what thoughts others might have on equipment/methods to determine these characteristics experimentally.

Any insight/suggestions you would be willing to provide would be greatly appreciated.

Thanks.
 
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When balancing rotating objects the entries in the tensor corresponding to moments of inertia can be balanced by static balancing. Those coresponding to product of inertia can only be balanced by dynamic balancing.

see this thread for an explanation, in particular posts 7 and 8

https://www.physicsforums.com/showthread.php?t=401927&highlight=product+inertia

So your experiment should involve static and dynamic balancing.

go well
 
I have created a static balancing experiment to determine the center of mass of this object.

However, I am having trouble creating a "dynamic balancing" project to find the Inertia Tensor. I believe this is most likely due to my lack of understanding of the theory behind what these properties really mean. I reviewed the other thread and found your diagram helpful in differentiating between principle moments of inertia (Ixx) and products of inertia (Ixy). I was hoping you might be able to give me some examples as to how I could complete a dynamic balancing scenario and what data would need to be monitored to calculate the inertia tensor.

Thanks again.
 
landong said:
Hello All,

I am trying to create an experiment to determine the center of mass and inertia tensor of an aribtrary object. This object is small (softball size), and non symmetrical on all axis. I have some thoughts concerning gyroscopes and accelorameters, but am curious to see what thoughts others might have on equipment/methods to determine these characteristics experimentally.

Any insight/suggestions you would be willing to provide would be greatly appreciated.

Thanks.

Finding the center of mass is easy- hang the object sequentially from three points, drawing a line from where you hang the object straight down. The lines intersect at the center of mass.

Getting the principal axis of the moment of inertia can be found here:

https://www.physicsforums.com/attachment.php?attachmentid=13128&d=1205872956

(Shamelessly stolen from Fred Garvin)

Or buy something:

http://www.space-electronics.com/Products/moment_of_inertia_instruments.php
http://www.idicb.com/moimeas.htm
 
Last edited by a moderator:
When considering the experiment in:

https://www.physicsforums.com/attachm...8&d=1205872956

Would the stiffness of the wires used not come into play?

Also, this would give you the moments of inertia about the principle axis: Ixx, Iyy, Izz

How could the remaining factors of the inertia tensor be found (Ixy=Iyx, Ixz=Izx, & Iyz=Izy)?

Thanks for your help.
 
Last edited by a moderator:

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