Rotational Dynamics / Moment of Inertia Question

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Homework Help Overview

The discussion revolves around the moment of inertia of an oxygen molecule, specifically estimating the effective distance between its two atoms based on given mass and moment of inertia values. The subject area includes concepts from rotational dynamics and geometry.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the calculated radius and the actual distance between the atoms, questioning the geometric interpretation of the radius. There are attempts to clarify the definitions of moment of inertia and moment arm, as well as to relate them to the problem at hand.

Discussion Status

Participants are actively engaging with the problem, raising questions about the definitions and relationships involved. Some have identified potential misunderstandings regarding the use of moment of inertia in geometric equations. There is a recognition of the need to clarify the roles of different variables in the context of the problem.

Contextual Notes

There appears to be confusion regarding the application of trigonometric relationships and the distinction between moment of inertia and moment arm, which may affect the interpretation of the problem. Participants are working within the constraints of the information provided and the definitions of physical quantities involved.

Arcarius
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Homework Statement


An oxygen molecule consists of two oxygen atoms whose total mass is 5.3x10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. From this data, estimate the effective distance between the atoms.

Homework Equations


## I = M1R^2 + M2R^2 ##

The Attempt at a Solution


I = (M1+M2)R^2
1.9 x 10^-46 kg*m^2 = (5.3 x 10^-26kg)R^2
R = 5.99 x 10^-11 m

Although I got that this is the radius, this is not the answer to the problem. I'm not exactly sure what I did wrong, as it seems right to me. Could anyone check my work? Thanks!
 
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Geometrically, what do you mean by "radius" here? How does this radius relate to the distance between the atoms?
 
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TSny said:
Geometrically, what do you mean by "radius" here. How does this radius relate to the distance between the atoms?

OH. Ugh, stupid mistake on my part! I used trig and got D to be 1.20 x 10^-10 m.
Thanks!
 
trig? How?
 
a209f0bb1bd1fb3d67d28f80a53a8df9.png

This is the diagram I drew, and you get that D/2 = sqrt(R^2 - I^2).
I then just solved for D, and it actually turned out to be approximately 2R.
 
Hmm. I imagine an oxygen molecule as being a little "dumbbell". What is "I" in your drawing?
 

Attachments

  • Oxygen.png
    Oxygen.png
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TSny said:
Hmm. I imagine an oxygen molecule as being a little "dumbbell". What is "I" in your drawing?

I had I as the Moment of Inertia.
 
When you wrote the equation D/2 = sqrt(R^2 - I^2), does "I" represent moment of inertia? If so, do you see a problem with that? Note that I is not a distance, and therefore cannot be used as one side of a right triangle.
 
TSny said:
When you wrote the equation D/2 = sqrt(R^2 - I^2), does "I" represent moment of inertia? If so, do you see a problem with that? Note that I is not a distance, and therefore cannot be used as one side of a right triangle.

Hmm, I see what you mean. I seem to have confused the moment of Inertia with the Moment Arm. In that case, I'm not sure how to use the information I have to get an answer :/
 
  • #10
What is the meaning of the ##\small R\:##'s in the formula ##\small I = m_1R_1^2 + m_2R^2## for the moment of inertia? Would you be able to label ##\small R_1## and ##\small R_2## in the figure of the oxygen molecule that I posted earlier?
 
  • #11
TSny said:
What is the meaning of the ##\small R\:##'s in the formula ##\small I = m_1R_1^2 + m_2R^2## for the moment of inertia? Would you be able to label ##\small R_1## and ##\small R_2## in the figure of the oxygen molecule that I posted earlier?

Ohhh I see. So it is 2R, I was just lucky that the numbers worked out when I did it my way.
 

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