Contact mechanics - Thrust bearing

[curiousPep]

Homework Statement

Thrust bearing: angular velocity of cage = angular velocity of plate/2

Relevant Equations

Not any

Hello,

I am doing some contact mechanics and I had an example in my Lecture notes about a simple thrust bearing with three balls where the bottom plate is stationary, the top plate rotates with angular velocity w, and the cage rotates with angular speed Ω.
It says by inspection Ω =w/2 but I can's see how this is valid.
I was not given any other data and the sketch provided is not useful, it's just the front view of the bearing without any additional info.

Thank you!

 

[berkeman]

It still might be useful to post the diagram, but it probably looks like the typical thrust ball bearing assembly like what is shown on Wikipedia.

Since the ball bearings are in contact with both the upper and lower plates, what is the linear velocity of each of the ball bearings? And how does that relate to their angular frequency about the central axis?

https://en.wikipedia.org/wiki/Thrust_bearing

 

[Dr.D]

As per Berkeman's figure, just remember that the balls roll without slip on both the upper and lower plates. This should give you the necessary information easily.

 

[Lnewqban]

https://www.me.psu.edu/cimbala/Learning/Fluid/Fluid_Prop/img00005.gif

 

[Dr.D]

I think the figure posted by @Lnewqban is actually intended to show the velocity gradient in a fluid flow. It just happens to fit this rolling situation, but that is purely coincidence.

 

[Lnewqban]

Think of the tangential velocity of the cage as the velocity of the center of mass of one of the balls or rollers, which is located halfway between the two tracks or rotating rings.

You can see the different velocities of cage and top track in the following video:
Please, read this excellent tutorial on rolling:
https://www.physicsforums.com/insights/explaining-rolling-motion/

:)