# Angular momentum

Hello!
http://img151.imageshack.us/img151/6571/cques1vd5.gif [Broken]

1. Homework Statement
A particle with mass m is thrown in lateral speed $$V_0$$ inside a hollow half-ball with radius $$R$$. At the beginning of it's motion the ball has an angle of $$\theta_0$$ from the perpendicular.
The gravitational force will pull the particle toward the center of the ball, while the centrifugal force will push it outwards.
Calculate the speed $$V_0$$, as a function of $$\theta_0$$, needed for the particle to reach the top of the half-ball in the peek of its motion.
Important! there's no string attached to the ball. The line on the image just indicates the radius.
2. Homework Equations
$$\overline J=m\overline r \times \overline v$$
$$\overline \omega=\overline{ \omega_0} + \overline\alpha t$$

3. The Attempt at a Solution

Well, the problem is I don't understand the forces involved.
I know there some sort of $$J_0$$ here, because there's an $$\overline r$$ and a $$\overline v$$. I can also draw a forces equation. Then there's the Normal force against mg and centrifugal force (btw - can I use the centripetal force instead?), but I don't quite know how to combine the two - F and J - together.

Thank you.

I thought of something: there are three forces: $$N, mg, \frac{mv^2}{R}$$.
also, I can do something like this: $$\Delta J = J_{end}-J_{start}$$, and $$J_{end}=0$$, because on the peak of the motions happens when v=0. also, $$J_{start}=mv_0R(sin\theta+cos\theta)$$.
and also $$\frac{dJ}{dt}=r \times F$$
so if I only knew how to play the forces right, I would have it.
Is it correct? if so, how do I know the force equation?

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