Stability of rigid body rotation about different axes

[Leo Liu]

Homework Statement

Below

Relevant Equations

NA

We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia. Why is it so?

 

[Steve4Physics]

We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy. However, for this question involving a rigid body, the most stable axis is the one with the lowest moment of inertia. Why is it so?

I'm no expert but I don't follow what you have written. If you look-up 'tennis racket theorem' you should find it helpful.

 

[Leo Liu]

I'm no expert but I don't follow what you have written. If you look-up 'tennis racket theorem' you should find it helpful.

Here is my reasoning I came up with after looking at the wiki article:
This object has two axes whose inertias are equal. So the rotation about either of these axes is unstable. If we apply euler's equations to this question, the functions of the angles will not show periodicity and will diverge; thus it is unstable.
Your reply is helpful. Thanks.

 

[haruspex]

We know that for a non-rigid body, the most stable type of rotation of it is the rotation about the axis with the maximum momentum of inertia and thus the lowest kinetic energy.

We do? I would not have thought one could be so general about rotation of non-rigid bodies.
For rigid bodies, the max and min are both stable.

This object has two axes whose inertias are equal.

Not so.

 

[Steve4Physics]

This object has two axes whose inertias are equal.

The question says the thickness is negligible. So we can treat the object as a lamina and use the perpendicular axis theorem. That should help you to establish the 3 moments of inertia are different and their relative sizes.

 

[Leo Liu]

We do? I would not have thought one could be so general about rotation of non-rigid bodies.
For rigid bodies, the max and min are both stable.

Well I was thinking that a non rigid body might dissipate energy through heat. But yeah what I said was too absolute.

Not so.

Sorry just realized they are disks as opposed to spheres.