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1. The problem statement, all variables and given/known data

A bowling ball is thrown down the alley with speed [tex] v_0 [/tex]. Initially, it slides without rolling, but due to friction, it begins to roll. Show that it's speed when it rolls without sliding is [tex] 5/7 v_0 [/tex]

2. Relevant equations

[tex] \tau = \vec R \times \vec f[/tex] where f is the force friction.

[tex] \vec L = \vec R \times M\vec V[/tex]

[tex] \vec v_f = \vec a t +\vec v_0 [/tex]

3. The attempt at a solution

I don't understand what is really going on conceptually when it goes from sliding to rolling.

I know that when it slides, it's kinetic friction, and when it slides, it's static friction.

So, there must be something that makes the bowling ball go from kinetic to static friction.

What that is, is where I go lost.

So I drew my FBD's. I set the origin along the axis of friction.

As it slides, there's gravity, the normal and kinetic friction in the usual places.

As it rolls, it's the same as above, but with static friction force and an arrow showing angular momentum.

Initially, it had no angular momentum because [tex] \vec L_0 = I_o \omega[/tex] , but [tex]\omega = 0 [/tex] initally ([tex] \omega [/tex]is angular velocity)

Thus, angular momentum would just be [tex] \vec L = \vec R \times M\vec V[/tex].

I know there's torque being applied due to friction which would be equal to rf*sin(theta).

Thereafter, I just wrote a bunch of equations down and I tried to see what would happen if I tried to solve for the force of friction using torque, but that leads no where. I tried going through linear energy and linear momentum, but that leads no where since I don't know under what condition it would make the bowling ball start rolling.

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# Homework Help: Angular Momentum - Bowling ball

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