Solving Rolling & Slipping Homework Problem

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The discussion revolves around a physics homework problem involving a billiard ball experiencing rolling and slipping. Key points include the need to calculate how long the ball slides before rolling without slipping, the distance it slides, and its speed upon transitioning to rolling. The student expresses confusion about applying relevant equations, particularly regarding kinetic energy loss due to friction and the relationship between linear and angular motion. Ultimately, the student resolves their own confusion by recognizing the conditions for rolling without slipping, specifically that the velocity at the contact point is zero when rolling begins. The conversation highlights the complexities of dynamics in rotational motion and the importance of understanding friction's role.
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Homework Statement


"A 0.18-kg billiard ball whose radius is 2.8 cm is given a sharp blow by a cue stick. The applied force is horizontal and the line of action of the force passes through the center of the ball. The speed of the ball just after the blow is 3.9 m/s and the coefficient of kinetic friction between the ball and the billiard table is 0.64."
How long does the ball slide before it begins to roll without slipping?
How far does it slide?
What is its speed once it begins rolling without slipping?

Homework Equations


translational kinetic=(1/2)mv^2 Rotational kinetic = (1/2)Iω^2
(when rotating without slipping) v=rω a=rα
Force of friction = force normal * coefficient of friction
Iα=r x F
L= r x p = rmvsin θ (i'm not sure if that is useful yet)

The Attempt at a Solution


I know that it's losing kinetic energy to friction
Force of friction*distance to point where it begins rotating
so I know that after that amount of energy loss... v=rω a=rα will hold true
but I don't know what to do with this...

The net force should just be the force of friction right? so a= Ff/m
so vf=vi+at

I'm confused as to what to do with any of this... it seems like I'm missing something...

I have (1/2)mVi^2=Ff*Δx+.7mVf^2 (added rotational and kinetic assuming that it is rotating)
and that's about all I can do I rearranged somethings and got about .7 seconds for the time. . . but I'm pretty sure that is wrong...

direction please?
 
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Hope you don't mind me bumping it (I'll compensate by adding some more ideas I have...I'm still working on it and failing haha)
I was thinking about the point of contact...when it begins to roll without slippage, the velocity at that point is 0 right? but with slipping...the sum of the vectors is NOT 0...it's v translation+r(omega) right? could I just use the angular acceleration I have to fine when r(omega) = v?
 
I solved my own problem =DDDD sorry guys...I'm stupid... maybe next time when it's really hard you guys will be interested enough to help? haha
 

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