Uniform solid sphere rolling on inclined plane

[antiparticle]

Homework Statement

A uniform solid sphere,rolls without slipping on a horizontal surface with an angular velocity $$\omega$$,meets a rough inclined plane of incination 60(degrees).The sphere starts pure rolling up the plane with an angular velocity.Find the new angular velocity .

Homework Equations

Angular momentum conservation about point of contact with the incline.

The Attempt at a Solution

 

[Quinzio]

That means that the sphere has to give up some of its rotational energy to acquire a velocity in a direction it hadn't before.
Find a relationship between momentum and kinetic energy and then resolve.