How High to Start a Ball so it Rolls Around a Loop-the-Loop Without Falling Off

Here is a slight variation of another loop-the-loop problem, which typically is a block sliding down a hill and around the loop.  Instead of just sliding with no friction, what if we put a ball on the track so it rolls without slipping...how will the height compare to that of the sliding block?

We would guess that, conceptually, a rolling ball might have to start higher than a block.  Why?  Because some energy is needed for the spinning of the ball.  Without a boost in height, the translational speed of the ball will be too small to stay on the loop all the way around.

So check this out.  It has rotations, circular motion, force diagrams, and conservation of energy all in one problem!  I hope it makes a bit of sense for you.