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

#1
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 , what is the velocity of the pipe relative to the table once it travels the length of the sheet?

It takes for the paper to be displaced by , at which point its speed is .
Since the pipe is rolling without slipping, then so .
The moment of inertia of the pipe is .

I'm told the angular momentum of the pipe is 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?

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#2
Resolved, the pipe is rolling without slipping, but the acceleration of the paper is at the bottom of the pipe, so instead of .
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8 months ago
#3
It's worse than that... it's physics, Jim!
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