Center of Mass and Inertia Tensor Experimentation

In summary, the conversation discusses creating an experiment to determine the center of mass and inertia tensor of an arbitrary object. The object in question is small, non-symmetrical, and multiple methods are suggested such as using gyroscopes and accelerometers. The discussion also touches on the use of static and dynamic balancing in determining the inertia tensor, with additional resources provided for further understanding. Questions are raised about the stiffness of wires and how to calculate the remaining factors of the inertia tensor.
  • #1
landong
3
0
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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  • #2
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
 
  • #3
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.
 
  • #4
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:
  • #5
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:

Related to Center of Mass and Inertia Tensor Experimentation

1. What is the purpose of a Center of Mass and Inertia Tensor Experimentation?

The purpose of a Center of Mass and Inertia Tensor Experimentation is to determine the distribution of mass and moments of inertia of a physical object. This information is crucial in understanding the object's stability and how it will respond to external forces.

2. How is the center of mass of an object calculated?

The center of mass of an object is calculated by finding the weighted average of the positions of all the individual particles that make up the object. This can be done mathematically using the mass and position coordinates of each particle.

3. What is the significance of the inertia tensor in experimentation?

The inertia tensor is a mathematical representation of an object's mass distribution. It provides information about an object's resistance to rotational motion and can be used to calculate its moments of inertia. This is important in understanding an object's dynamics and predicting its behavior under different conditions.

4. How can the center of mass and inertia tensor be experimentally determined?

The center of mass and inertia tensor can be experimentally determined by performing physical experiments such as balancing the object on a pivot point and measuring its oscillation period. Other methods involve using specialized equipment such as a torsion pendulum or a rotational inertia apparatus.

5. What are some real-world applications of Center of Mass and Inertia Tensor Experimentation?

Center of Mass and Inertia Tensor Experimentation has many practical applications, including designing stable structures, predicting the behavior of moving objects, and creating accurate simulations in fields such as engineering, physics, and robotics. It is also used in sports to optimize the performance of equipment and in medicine to understand the human body's movement and balance.

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