1. The problem statement, all variables and given/known data A billiard ball of mass [itex]M[/itex] and radius [itex]R[/itex] is hit by a cue as shown in the figure. http://i.imgur.com/vJ7qB8W.png The blow can be thought as an impulse [itex]J[/itex] of given value, and let [itex]μ[/itex] be the coefficient of static friction. 2. Relevant equations Find the maximum angle for which the ball's initial velocity isn't null. 3. The attempt at a solution It seems I have a big, serious doubt here. From the definition of Impulse I know that [itex]J=\Delta p[/itex] (1) [itex]JRsin(θ)= I\Deltaω[/itex] , with I being the moment of inertia of the body. Since the body is at rest before being hit we can just write [itex]p[/itex] and [itex]ω[/itex] to indicate the initial values of the rotational and translational velocities. This is where I get stuck: I fail to comprehend how to impose the non-null initial velocity, and thus how to get the disequation which will give me the maximum value of the angle. The problem should be solved once I know which formula to use. I know the velocity of a given point P is [itex]V= v_r+v_t=v_g+ωr_P[/itex], (rotational and traslational components, [itex]v_g[/itex] stands for the velocity of the c.o.m.) equation (1) can lead me to the value of [itex]v_g[/itex], but what about the other term? That said the problem is saying that [itex]V[/itex], hence its magnitude, isn't zero, but I'm having trouble putting this into pratice. I know this is a vague answer but I'm completely lost and I can't find useful examples on my notes. The problem seems very easy, yet I can't solve it and this is pretty depressing; what am I forgetting about? Forgive me for the bad pic but it's the best reproduction I can do at the moment, if you don't understand something feel free to say it. Thank you for your help.