# Moment of inertia

## Main Question or Discussion Point

Why the moment of inertia of a molecule about the bond axis is small enough to ignore ?

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Simon Bridge
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Try calculating it and see.

Try calculating it and see.
I really don't have any idea.Please guide me.

Bystander
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Where is the mass of an atom located?

Where is the mass of an atom located?
throughout the atom.But being more technical i think where center of mass is present.

Simon Bridge
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How do you normally calculate the moment of inertia?
What would the distribution of mass in a diatomic molecule look like - roughly?

Bystander
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throughout the atom
"????" Back up. Describe the structure of an atom.

"????" Back up. Describe the structure of an atom.
sorry i think the nucleus contain all mass as electrons have negligible mass.

Bystander
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Better. What's the diameter of a typical nucleus, or has that been covered for you at all?

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.

Better. What's the diameter of a typical nucleus, or has that been covered for you at all?

Bystander
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Sounds about right. What's nuclear mass x 1/2 of that squared?

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?

I normally calculate moment of inertia as total mass multiplied by Distance between the axis and rotation in m..

Bystander
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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.

That's an end point of a bond axis.
Sorry i am talking about a molecule.Here x axis is bond axis.

Bystander
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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.

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.

[QUOTE="Bystander, post: 4940685, member: 50"the bond axis is the line connecting the nuclei of the two atoms,

Now is x axis bond axis?

[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.

No, your black line (the bond) is (lies along) the bond axis.
That's what i mean. Is black line bond axis?

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.

No, your black line (the bond) is (lies along) the bond axis.

#### Attachments

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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.

Right?