How High Must a Cylinder Roll to Loop-the-Loop?

[GemmaN]

In this problem you will consider the motion of a cylinder of radius r_1 that is rolled from a certain height h so that it "loops the loop," that is, rolls around the track with a loop of radius r_2. The cylinder rolls without slipping.

It looks like your standard matchbox car loop.

I need to find the minimum height h that will allow a solid cylinder of mass m and radius r_1 to loop the loop of radius r_2. "Express h in terms of the radius r_2 of the loop."

I am not quite getting a certain portion of this. I know the important part of this problem is when the cylinder is at the top of the loop.
Now, at this point, I know it has a potential energy of 2*r_2*m*g
To stay on the track without slipping, I think I need v = R*omega
At the top part of the track, the cylinder is upside down, and has no normal force... so weight matters?

I may need to use this: K = 1/2Mv_cm^2 + 1/2 I_cm*omega^2

mgh = (2)r_2(mg) + KE? + ?

I am a bit confused at this point. How am I suppose to put this together?

 

[physics girl phd]

You are correct in that the "important part of this problem is when the cylinder is at the top of the loop".

Hint -- draw a free body diagram for the system at that location.