How to Calculate the Speed of a Solid Sphere on a Frictionless Incline?

[Momentum09]

Homework Statement

A solid sphere of radius 20cm is positioned at the top of an incline that makes 22 degrees angle with the horizontal. This initial position of the sphere is a vertical distance 1.8m above its position when at the bottom of the incline. Moment of inertia of a sphere with respect to an axis through its center is 2/3MR^2. Calculate the speed of the sphere when it reaches the bottom of the incline in the case where it slips frictionlessly without rolling.

Homework Equations

mgh = 1/2Iw^2 + 1/2mv^2

The Attempt at a Solution

I know how to calculate the speed when the object rolls down without slipping, but what do I do if it does? if there a formula? Thank you for your help!

 

[Doc Al]

If it slips without rolling then there is no rotational KE, just translational KE.

If it rolls without slipping then there is both rotational and translational KE. The are related by the condition for "rolling without slipping", which is: $v = \omega r$.

 

[Momentum09]

Thank you so much!