What is the velocity of the ice cube when it loses contact with the sphere?

[faidros]

Hello,

I've encountered some problems while doing a mechanics project, and was hoping for some help here.
The problem is what follows:

An icecube starts to move at the top of a half spherical building (start velocity 0, no friction, and can be regarded as a particle). What's the icecube's velocity at the time it looses contact with the sphere and begins to fall?

Any ideas?

 

[faidros]

The centripetal force for the particle is F=(mv^2)/R
Could this force be expressed as F = ma, where a is the acceleration in a cylindrical coordinate system?
i.e:
r=R(cosa, sina)
v=Ra'(-sina, cosa)
a=Ra''(-cosa,-sina) <----

Am I way off here?
Does anybody have an approach on this problem? Any ideas how to express the angle between the vertical and the particle in terms of time and gravity?

thanks for any help