Moment of Inertia: Ignoring Small Bond Axis Molecule

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The moment of inertia of a molecule about its bond axis is generally small enough to ignore due to the significant difference in scale between bond lengths and nuclear dimensions. Calculations show that the moment of inertia about the bond axis is on the order of 10^-10 compared to moments of inertia about axes perpendicular to the bond axis. The bond length, which is the distance between atomic nuclei, typically ranges from 1 x 10^-10 to 2 x 10^-10 meters, while nuclear diameters are on the order of 10^-30 meters. This disparity in dimensions results in a negligible contribution to the overall moment of inertia when considering rotation about the bond axis. Understanding these concepts is crucial for accurately calculating molecular dynamics and rotational behavior.
gracy
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Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?
 
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Try calculating it and see.
 
Simon Bridge said:
Try calculating it and see.
I really don't have any idea.Please guide me.
 
Where is the mass of an atom located?
 
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Bystander said:
Where is the mass of an atom located?
throughout the atom.But being more technical i think where center of mass is present.
 
How do you normally calculate the moment of inertia?
What would the distribution of mass in a diatomic molecule look like - roughly?
 
gracy said:
throughout the atom
"?" Back up. Describe the structure of an atom.
 
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Bystander said:
"?" Back up. Describe the structure of an atom.
sorry i think the nucleus contain all mass as electrons have negligible mass.
 
Better. What's the diameter of a typical nucleus, or has that been covered for you at all?
 
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  • #10
Simon Bridge said:
How do you normally calculate the moment of inertia?
What would the distribution of mass in a diatomic molecule look like - roughly?
I normally calculate moment of inertia as total mass multiplied by distance square.
 
  • #11
Bystander said:
Better. What's the diameter of a typical nucleus, or has that been covered for you at all?
about 1.75 fm.
 
  • #12
Sounds about right. What's nuclear mass x 1/2 of that squared?
 
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  • #13
Bystander said:
What's nuclear mass x 1/2 of that squared?
Sorry I didn't understand.Nuclear mass would depend on atom of which element we are taking.
Bystander said:
1/2 of that squared?
squared of what?
 
  • #14
I normally calculate moment of inertia as total mass multiplied by Distance between the axis and rotation in m..
 
  • #15
gracy said:
Sorry I didn't understand.Nuclear mass would depend on atom of which element we are taking.
Pick an atom.

gracy said:
squared of what?
"What?" The nuclear diameter. That's an end point of a bond axis.
 
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  • #16
Bystander said:
That's an end point of a bond axis.
Sorry i am talking about a molecule.Here x-axis is bond axis.
upload_2014-12-10_11-51-26-png.76442.png
 
  • #17
No, that is one of three rotational axes directed at right angles to one another through the center of mass of the molecule; the bond axis is the line connecting the nuclei of the two atoms, and is the one axis of the three that you're interested in for this problem.
 
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  • #18
Bystander said:
No, that is one of three rotational axes directed at right angles to one another through the center of mass of the molecule; the bond axis is the line connecting the nuclei of the two atoms, and is the one axis of the three that you're interested in for this problem.
Bystander is correct, the axis you have as your x-axis is one with a non-negligible moment of inertia. There would also be one perpendicular to this and the axis along the bond, which also has a non-negligible moment of inertia, this is why diatomic gases have two rotational degrees of freedom. The bond axis is that which joins the two nuclei.
 
  • #19
[QUOTE="Bystander, post: 4940685, member: 50"the bond axis is the line connecting the nuclei of the two atoms,
upload_2014-12-10_19-45-17.png

Now is x-axis bond axis?
 
  • #20
gracy said:
[QUOTE="Bystander, post: 4940685, member: 50"the bond axis is the line connecting the nuclei of the two atoms,
View attachment 76453
Now is x-axis bond axis?
No, your black line (the bond) is (lies along) the bond axis.
 
  • #21
Vagn said:
No, your black line (the bond) is (lies along) the bond axis.
That's what i mean. Is black line bond axis?
 
  • #22
gracy said:
That's what i mean. Is black line bond axis?
The black line joining the two blue atoms is the bond axis. Your diagram is confusing as the arrow suggests your x-axis is vertical and perpendicular to the bond.
 
  • #23
Vagn said:
No, your black line (the bond) is (lies along) the bond axis.
 

Attachments

  • upload_2014-12-10_20-6-52.png
    upload_2014-12-10_20-6-52.png
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  • #24
Vagn said:
The black line joining the two blue atoms is the bond axis. Your diagram is confusing as the arrow suggests your x-axis is vertical and perpendicular to the bond.
upload_2014-12-10_20-7-57.png

Right?
 
  • #25
  • #26
Vagn said:
That's better.
Now how to proceed further in order to get the answer .
 
  • #27
What's the maximum distance of the nuclear mass from that axis?
 
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  • #28
Bystander said:
What's the maximum distance of the nuclear mass from that axis?
here (in the image i have given)there are two atoms( after all i am referring to diatomic molecule)nuclear mass of which one?
 
  • #29
Both of them. How far are they from the axis you've drawn?
 
  • #30
Bystander said:
Both of them. How far are they from the axis you've drawn?
upload_2014-12-10_20-22-1.png

I think answer would be ~nearly zero.
 

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