Center of Mass and Inertia Tensor Experimentation

AI Thread Summary
An experiment is being developed to determine the center of mass and inertia tensor of a small, non-symmetrical object. The discussion highlights the importance of both static and dynamic balancing methods, with static balancing already implemented for finding the center of mass. Challenges remain in creating a dynamic balancing project to accurately calculate the inertia tensor, particularly due to a lack of understanding of the underlying theory. Suggestions include using gyroscopes and accelerometers, as well as referencing existing resources for guidance on principal moments and products of inertia. The conversation emphasizes the need for clarity on how to measure the off-diagonal components of the inertia tensor.
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
 
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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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