# Dynamics in a circular disc dilemma

Experimental setup:

Imagine a circular disc kept horizontally with a frictionless groove along its diameter, in a uniform gravitational field perpendicular to disc. There is a ball in the groove currently at the center of disc. The circular disc now starts rotating with constant angular velocity $$\omega$$.

Predictions:

According to me, the ball must start moving away from the center along the groove.

Conclusions/Discussion:

Both rotating frame and non rotating frame must see ball moving and eventually fall from disc.

According to rotating frame of reference of disc, the dynamics of ball can be easily by applying centrifugal force as it is applied in rotating frame.

But according to non rotating frame of reference, the dynamics of the ball cannot be explained by centrifugal force and neither centripetal force

So, how is the dynamics of ball explained with respect to non rotating frame?

What force is pushing the ball with respect to non rotating frame?

Is there any flaws in my predictions and conclusions? Any help is massively appreciated.

• The way you posit the problem is incomplete. What about friction (or other forces) acting tangentially and not just radially?
– Gert
Commented Feb 9, 2021 at 8:54
• I have mentioned that groove is frictionless in which ball is moving. Commented Feb 9, 2021 at 8:55
• Commented Feb 9, 2021 at 9:01

"Both rotating frame and non rotating frame must see ball moving and eventually fall from disc".

I am assuming that the radius cannot accommodate the velocity of the rotating ball in your setup and that the groove can provide a tangential force. In the case of your experimental setup, in the non-rotating frame, the tangential force provided by the groove will allow your ball to move in a circular path. In this case, you can think of the tangential force the ball exerts on the grove as your "force causing circular motion"(but it is not centripetal force) and the reaction force as a type of pseudo force such as centrifugal force. The ball will move in a straight line with respect to the "force causing the circular motion" for the rotating frame, but not in a straight line as it travels along the groove with respect to the nonrotating frame. For the nonrotating frame, the object will follow an approximately parabolic path.

• But please clarify that which force I acting on ball, making it move according to non rotating frame. Commented Feb 9, 2021 at 8:58
• To get a meaningful answer to that question, change to a set up where you know the ball will move, in any frame.
– Gert
Commented Feb 9, 2021 at 9:02
• @Gert What do you mean? Commented Feb 9, 2021 at 9:22
• @KshitijKumar In your question you assumed the ball would somehow move. But it doesn't because there's no friction whatsoever. So it's bad scenario to discuss movement of the ball in other ref. frames. If it doesn't move in one, solutions in the others are essentially trivial because you already had your answer.
– Gert
Commented Feb 9, 2021 at 9:35