Motion of a particle constrained on a rotating rod

A sphere of neglectable radius is placed on a very long and frictionless rod (which we can approximate to a straight line) on which it is able to move. The rod rotates around one of its end points with constant angular velocity $omega$. Find:

1. Whether the sphere gets closer or farther from the fixed end point
2. The direction and orientation of the total force acting on the particle in an inertial frame of reference (e.g. that whose origin lies on the fixed end point of the rod)
3. The equation of motion of the particle in the same reference frame.

I don’t know how to answer 1. I might say it moves towards the centre, but I have poor physical intuition.

As for 2, the only force acting on the particle is the vincular reaction of the rod, which constrains the particle to move over the rod itself. But there is no explicit formula for vincular forces: their value can be found only if the total acceleration is known, which is after all what we’re trying to evaluate in the first place…

Perhaps conservation of energy or angular momentum could help? Constraint forces do no work, so the potential energy would be null at all times…but of course we know nothing about kinetic energy, and the same for momentum. The only thing we know is that $theta (t)=omega t$, where $theta$ is the angle between the $x$ axis and the position vector. Thus, we have one of two polar coordinates. How to find the other one, however, I have no clue.

Could you give me a hint on how to approach this problem?