Angular impulse of rolling ball

AI Thread Summary
The discussion focuses on using angular impulse to determine the velocity at which a sliding sphere transitions to pure rolling upon encountering a frictional surface. Participants highlight errors in the initial formulation, particularly regarding the notation and the relationship between initial and final velocities. There is confusion about the implications of linear momentum being greater than the impulse applied. Clarifying the distinction between initial and final speeds could help resolve misunderstandings. The conversation emphasizes the need for precise definitions and relationships in physics problems involving motion and friction.
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In the following, we have a sliding sphere, when it meets a floor with friction.

I want to use the angular impulse method to find an expression of the v when pure rolling starts.

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[sorry I have no idea how to type in latex.]

This is obviously incorrect.
But I can't find out what's wrong. anyone?
 
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Why is that obviously wrong? I at least could follow it. (Small note: you changed from r to R in the problem. Also I think Vi should equal Vi not Vi=V because if Vi=V that's like Vi=Vf, but that's more of a typo.)
 
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it's wrong cos it states that mv is larger tahn the impulse given.
 
?? Kind of following. Why does that matter? The value of mv can be bigger than the linear impulse in this problem. (Note: where mv=mVfinal)
 
It might become clearer if you properly distinguish initial and final linear speeds (u, v perhaps) and get the relationship between them.
 

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