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

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

A particle with mass m is thrown in lateral speed [tex]V_0[/tex] inside a hollow half-ball with radius [tex]R[/tex]. At the beginning of it's motion the ball has an angle of [tex]\theta_0[/tex] 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 [tex]V_0[/tex], as a function of [tex]\theta_0[/tex], 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. Relevant equations

[tex]\overline J=m\overline r \times \overline v[/tex]

[tex]\overline \omega=\overline{ \omega_0} + \overline\alpha t[/tex]

3. The attempt at a solution

Well, the problem is I don't understand the forces involved.

I know there some sort of [tex]J_0[/tex] here, because there's an [tex]\overline r[/tex] and a [tex]\overline v[/tex]. 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.

[edit]

I thought of something: there are three forces: [tex]N, mg, \frac{mv^2}{R}[/tex].

also, I can do something like this: [tex]\Delta J = J_{end}-J_{start}[/tex], and [tex]J_{end}=0[/tex], because on the peak of the motions happens when v=0. also, [tex]J_{start}=mv_0R(sin\theta+cos\theta)[/tex].

and also [tex]\frac{dJ}{dt}=r \times F[/tex]

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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# Homework Help: Angular momentum

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