Help with rotational motion work

[Heisenburger]

Homework Statement

A billiards ball of mass M is initially motionless on a table when it is hit by a cue projecting it forward with speed V and no angular velocity. Find the speed of the ball when it eventually begins to roll. Assume the ball does not slip when it begins to roll. What proportion of the original kinetic energy is lost in the process? (The ball’s moment of inertia is 2Ma^2/5.)

Homework Equations

K=0.5mv^2
K=Iω^2
v=ωr

The Attempt at a Solution

k before = 0.5mv^2
after = Iw^2, where w=v/r

so proportion of energy lost = energy lost/original energy

=0.5mv^2-Iw^2 all over 0.5mv^2?

= 1- $\frac{2a^2}{5r^2}$

 

[Doc Al]

I assume they mean for you to find when the ball begins rolling without slipping. How can you find that final velocity of the ball's center of mass?

 

[Heisenburger]

I assume they mean for you to find when the ball begins rolling without slipping. How can you find that final velocity of the ball's center of mass?

I'm not sure, is it not the same as the start? or do i take into account energy lost before this?

 

[Doc Al]

I'm not sure, is it not the same as the start?

How can it be? What causes the ball to rotate is friction, which slows the translational speed as it increases the rotational speed. In the process, mechanical energy is lost.

or do i take into account energy lost before this?

Start by figuring out the final velocity, which will be less than the initial velocity. (There are several ways of doing this.)