### Particle Dynamics and Newton's Laws

On a circular hoop with radius $l$ there is a bead that can move freely without friction.
The hoop is rotated in a constant frequency $\omega$ around the horizontal axis.
1. What are the forces that act on the bead in equilibrium.
2. Find the angle $\theta$ in that state as a function of $\omega$.
3. What should be $\omega$ in order to move the bead to the center of the hoop? can the bead move beyond the center of the hoop?