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## Homework Statement

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.

## Homework Equations

Find the maximum angle for which the ball's initial velocity isn't null.

## 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.

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