Q:

Will ball slip or roll in this situation?

A ball rolling on a horizontal surface without slipping  encounters a curved incline as shown in diagram below.  The curved incline is smooth and frictionless.
Question
What will happen to the rolling ball on the curved incline and why? Will it continue to roll without slipping or will it move up the incline without rolling?
My take on this situation
I think the ball will continue rolling but with decreasing angular velocity and decreasing linear velocity of it's center.  The angular velocity will decrease because the gravity force mg acting vertically down will exert a clockwise torque about an axis passing through the point of contact of ball with incline and perpendicular to the incline plane (i.e. axis is perpendicular to the plane of paper). I am not sure about this explanation and observation.

A:

Without friction, $\omega$ and $v$ are decoupled, and the ball will climb up to $h_{2}=\frac{v^{2}}{2g}$ (when all translational kinetic energy is transformed into potential energy) and then fall back the curve. During this process, the rotation will be what it was when entering the curve.
When the it reaches the horizontal part again, there is necessarily slipping, since the translational velocity is still $v$ but in the other direction, and the angular velocity is $w$ as before.

