Can you help me with a 'contention' I have with my university supervisor? Apologies if this has been answered elsewhere.
I have a device that can be modeled as a wheel/tire with a ball inside (in 2D) - a vertical circular track with a ball which is able to roll freely inside. At rest, the ball is at the bottom of the vertical circle and that will be the angular position of the ball about the center of the wheel.
I want to understand the governing equations for the motion of the ball if the wheel is rotated.
My understanding is that if the wheel is rotated at a certain angular velocity, the ball will be dragged up one side until gravity pulls the ball back towards the zero position. The torque from the friction will cause the ball to roll. At a certain point it will achieve equilibrium, the ball will roll constantly towards the bottom of the circle but not move, maintaining an angular position ($\theta$) somewhere between 0 and 90 degrees - a bit like a hamster running in its wheel!
My question is if the ball is rolling fast enough to maintain its position inside a rotating track, does it experience a centrifugal force? Everything else being equal, would 2 balls of different masses roll at different theta positions? Is it possible to predict this value of theta for different balls?
Thanks for any help!