Motion of a ball along a groove on a rotating disk

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Discussion Overview

The discussion revolves around the motion of a ball placed in a groove on a rotating disk, specifically examining whether the ball will move along the groove when friction is absent. The scope includes conceptual reasoning and technical clarification regarding the dynamics involved in this scenario.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that a ball tightly placed in a groove on a rotating disk will move outwards due to the absence of friction.
  • One participant questions whether the original description intended to refer to the radius or diameter of the ball in relation to the groove's width, suggesting that this distinction affects the ball's interaction with the groove.
  • A participant argues that if the ball is fixed to the groove and the rotation is suddenly stopped, the ball would tend to move perpendicular to the radius due to inertia, but this motion would be hindered by the walls of the groove.
  • Another participant clarifies that "moving outwards" refers to increasing the distance from the center of rotation, emphasizing that without rotation, the ball will not move outwards.
  • A later reply references a homework problem from a mechanics text that resembles the discussed system, suggesting it may provide additional insights for analysis.

Areas of Agreement / Disagreement

Participants express differing views on the ball's motion along the groove, with some asserting it will move outwards while others challenge this notion based on the conditions described. The discussion remains unresolved regarding the exact nature of the ball's motion under the specified conditions.

Contextual Notes

Participants highlight potential confusion regarding the definitions of radius and diameter in the context of the ball and groove. There is also an acknowledgment of the role of inertia and the constraints imposed by the groove's walls, which are not fully resolved in the discussion.

NANDHU001
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Will a ball placed tightly (radius of ball=width of groove) in a groove(length of grove along radius) on a rotating disk have any motion along the groove. The frictional force is zero.
 
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NANDHU001 said:
Will a ball placed tightly (radius of ball=width of groove) in a groove(length of grove along radius) on a rotating disk have any motion along the groove. The frictional force is zero.
Yes, outwards.
 
It is not too important but, are you sure that you mean the radius of the ball equals the width of the groove and not the DIAMETER of the ball equals the width of the groove.
In the first case do you imagine the ball touching the bottom of the groove or riding along the edges of the groove.
Basically the ball will travel in a straight line tangential to the circle of its radius, this means you will see it roll along the groove I.e 'travel outwards'
 
Thanks, for pointing out the mistake, it was actually diameter I had in mind while using radius. But still I can't imagine how the ball should move outwards. I'll put the question in a different manner. Suppose the ball was fixed to the groove during the course of rotation, all of a sudden the rotation is stopped by an external agency and the ball is made free to move along the groove simultaneously. The ball will then have a tendency to move perpendicular to the radius(or groove) due to inertia, but isn't this tendency hindered by the walls of the groove.
 
NANDHU001 said:
But still I can't imagine how the ball should move outwards.
To clarify: By "move outwards" I meant increase the distance to the center of rotation, move radially relative to the table.
NANDHU001 said:
I'll put the question in a different manner ... rotation is stopped.
It's a different question, not a different manner. Without rotation it will not move outwards.
 
While A.T. thoroughly answered your question already, I remembered a homework problem from Kleppner's mechanics text that was similar to the system you were describing. Maybe it will be of interest to you: http://s24.postimg.org/j7tc6axsl/groove_disk.png

Toy around with the system as you see fit for your analysis purposes :).
 

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