Wobbling Disks: Thin Hoop vs Solid Disk

[nautikal]

What would wobble more easily... a thin hoop or a solid disk of the same mass? A solid disk will have a lower moment of inertia, but I'm not sure how this applies to wobbling.

I was just thinking about CD players and how they vibrate a lot from the discs wobbling. Would thickening the outer portion of the disc reduce wobbling by raising the inertia, or would wobbling be reduced by thinning the outer portion of the disc and lowering the inertia?

 

[pixel01]

The more inertia, the less wobble the top can be, that's why toy tops often be made like they are.

 

[jambaugh]

What causes wobble is when the center of rotation is not through the center of mass.

I don't think it will be a matter to first order which you choose. The amount of wobble will be proportional to the first moment, i.e. the mass times offset from center of mass. If in both cases the mass is the same then they'll both wobble the same for a given drilling error. Thickening the outer portion will add mass and increase wobble. Reducing the outer portion will lower it but this only because you're affecting the over-all mass while leaving the error in the balance point unchanged.

Your best bet would be to carefully trim the disks so that they are more perfectly balanced. But doing so will also potentially create points where cracking can occur and the disk could shatter under the tensile load of spinning.

Actually I think there's some elastic give in the actual player's bearing mounting which will allow the rotating system to settle into a rotation about the COM. Picture the circus acrobats who spin about their length from a rope held by their arms. This is an extreme example of what I'm talking about. The axle wobbles to allow the actual object to rotate about its COM. The faster it turns the less tolerance there is in this stabilizing effect. (The lovely circus acrobats will end up swinging in wide circles outside the rope instead of the rope making circles around them.)

There are other issues such as resonances between the rotational period and the period of oscillation for the mass of the disk and the elasticity of the bearing mounts. You may have noticed tire vibration which peaks at a certain speed but then decreases as you go faster.

I think principally the issue of CD wobble is a question of the player's tolerances and design. (You get what you pay for or more accurately no more than what you pay for.)