What factors affect the movement of a ball bearing attached to a spinning disc?

[MrShoe]

Hello everyone,

Being new here, and not a "Physics Guy" I wasn't sure where this should go, but General Physics seemed like the best bet.

Recently I've been thinking about the effects of circular motion on external objects, and I've hit dead end with one of my trains of thought.

Excuse the crude drawing, but this is what I'm looking at:

The above picture shows a round disc (meant to be perfectly round/balanced) attached to a drive shaft, with a blue ring on the outside containing a ball bearing. The ring would be a tube inside the outer perimeter of the disc (see below image):

As the disc starts to spin, I imagine that the bearing would also move, probably spinning in the opposite direction, but moving in the same direction. What I'd like to figure out is at what RPM would the bearing stop moving completely, and the factors that can and will change this.

For simplicity, let's say the disc has a diameter of 4" and the ball bearing has a mass of 0.5g. The drive shaft can spin from 0-600 RPM.

I'm sorry if this is vague, I tried to word it the best way I could. If anymore information is needed please let me know.

Thank you!

 

[tiny-tim]

Hello MrShoe! Welcome to PF!

The friction is always forward, so the ball will always move forward relative to the ground, but will always move, and roll, backward relative to the disc.

 

[MrShoe]

Ohh I see, thank you, but at what point will the ball stop rolling and stick to the outer edge? Or how would I go about finding that? Assuming that the bearing itself and the surface on the inside of the tube are both very smooth.

 

[tiny-tim]

Ohh I see, thank you, but at what point will the ball stop rolling and stick to the outer edge?

oh i see … you mean, like a centrifuge, which if it spins fast enough, things will stick to its outer wall?

no, the ball will still roll (backwards) whatever the speed, because the center of mass of the ball will always be a constant distance from the outer wall, no matter what position the ball is

(this is unlike say a cube, which once the centrifuge reaches a certain speed will be unable to "roll" because that would mean being on edge at times, and the distance to the centre of mass is √2 more in that position, and the "centrifugal force" prevents the centre of mass "rising that high")

there is no reason for the ball to stop rolling, at least until the pressure makes it so deformed that it becomes a bit cube-like

 

[MrShoe]

That makes a lot of sense, actually.

Thank you for the explanation!