Moment of inertia

  • Thread starter gracy
  • Start date
  • #1
2,486
83
Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?
 

Answers and Replies

  • #2
Simon Bridge
Science Advisor
Homework Helper
17,874
1,657
Try calculating it and see.
 
  • #3
2,486
83
Try calculating it and see.
I really don't have any idea.Please guide me.
 
  • #4
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Where is the mass of an atom located?
 
  • Like
Likes gracy
  • #5
2,486
83
Where is the mass of an atom located?
throughout the atom.But being more technical i think where center of mass is present.
 
  • #6
Simon Bridge
Science Advisor
Homework Helper
17,874
1,657
How do you normally calculate the moment of inertia?
What would the distribution of mass in a diatomic molecule look like - roughly?
 
  • #7
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
throughout the atom
"????" Back up. Describe the structure of an atom.
 
  • Like
Likes gracy
  • #8
2,486
83
"????" Back up. Describe the structure of an atom.
sorry i think the nucleus contain all mass as electrons have negligible mass.
 
  • #9
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Better. What's the diameter of a typical nucleus, or has that been covered for you at all?
 
  • Like
Likes gracy
  • #10
2,486
83
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
2,486
83
Better. What's the diameter of a typical nucleus, or has that been covered for you at all?
about 1.75 fm.
 
  • #12
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Sounds about right. What's nuclear mass x 1/2 of that squared?
 
  • Like
Likes gracy
  • #13
2,486
83
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.
1/2 of that squared?
squared of what?
 
  • #14
2,486
83
I normally calculate moment of inertia as total mass multiplied by Distance between the axis and rotation in m..
 
  • #15
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Sorry I didn't understand.Nuclear mass would depend on atom of which element we are taking.
Pick an atom.

squared of what?
"What?" The nuclear diameter. That's an end point of a bond axis.
 
  • Like
Likes gracy
  • #16
2,486
83
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
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
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.
 
  • Like
Likes gracy
  • #18
518
64
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
2,486
83
[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
518
64
[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
2,486
83
No, your black line (the bond) is (lies along) the bond axis.
That's what i mean. Is black line bond axis?
 
  • #22
518
64
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
2,486
83
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
    11.1 KB · Views: 418
  • #24
2,486
83
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?
 
  • #26
2,486
83
That's better.
Now how to proceed further in order to get the answer .
 
  • #27
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
What's the maximum distance of the nuclear mass from that axis?
 
  • Like
Likes gracy
  • #28
2,486
83
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
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Both of them. How far are they from the axis you've drawn?
 
  • #30
2,486
83
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.
 
  • #31
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Yes. This is the point of asking you what nuclear dimensions are; so, calculating moments of inertia for the three rotational axes of a molecule about its center of mass, you have two that square something of the same order of magnitude as the bond length (not half in general, because not all diatomic molecules are homonuclear), and a third moment that squares a distance the order of nuclear dimensions.
 
  • Like
Likes gracy
  • #32
2,486
83
This is the point of asking you what nuclear dimensions are; so, calculating moments of inertia for the three rotational axes of a molecule about its center of mass, you have two that square something of the same order of magnitude as the bond length (not half in general, because not all diatomic molecules are homonuclear), and a third moment that squares a distance the order of nuclear dimensions.
Sorry but i am not getting this post.
 
  • #33
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
Three questions: what size are bond lengths? What is typical nuclear diameter (radius)? What is the ratio of the squares of those two dimensions?
 
  • Like
Likes gracy
  • #34
2,486
83
bond length is the average distance between nuclei of two bonded atoms in a molecule. why are you asking for bond lengths?as there is only one ,right?[/QUOTE]
and why you have written radius inside the bracket after word diameter as these two are totally different.
 
  • #35
Bystander
Science Advisor
Homework Helper
Gold Member
5,353
1,431
You've got finals or midterms coming up, so I'll give you a break --- squaring bond lengths gives you something of the order of 10-20m2 and squaring nuclear diameter or radius gives you something of the order of 10-30m2. Multiplying those values time nuclear masses gives you moments of inertia. The moment of inertia about a bond axis is on the order of 10-10 that of the moments of inertia for rotations about axes perpendicular to the bond axis.
 
  • Like
Likes gracy

Related Threads on Moment of inertia

  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
3
Views
2K
Replies
1
Views
25K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
7
Views
1K
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
715
Top