A cylinder rolling due to the acceleration of the plane it's resting upon Watch

MartyO
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Suppose a pipe with thin walls is resting on a sheet of paper.
When the sheet of paper is accelerated to the left, the pipe starts to roll without slipping in a clockwise fashion.
If the sheet of paper is accelerated by a, what is the velocity of the pipe relative to the table once it travels the length l of the sheet?

It takes \Delta t = \sqrt{2 l / a} for the paper to be displaced by l, at which point its speed is - \sqrt{2 l a}.
Since the pipe is rolling without slipping, then v = r \omega so a = r \alpha.
The moment of inertia of the pipe is m r^2.

I'm told the angular momentum of the pipe is L = I \omega + mrv since it is a rigid body.

I can't help but think the pipe will have an angular speed but no horizontal speed relative to the ground, yet the pipe should have a horizontal speed to the left because it rolled on the paper.
What steps am I missing in order to solve this problem?

Thanks in advance!
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MartyO
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Resolved, the pipe is rolling without slipping, but the acceleration of the paper is at the bottom of the pipe, so v = 2 r \omega instead of v = r \omega.
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Vinny C
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It's worse than that... it's physics, Jim!
https://www.youtube.com/watch?v=M1pzN3CgANE
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