Motion of a ball along a groove on a rotating disk

[NANDHU001]

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.

 

[A.T.]

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.

 

[Emilyjoint]

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'

 

[NANDHU001]

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.

 

[A.T.]

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.

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.

 

[WannabeNewton]

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 :).