ok.. as a rule... i never solve questions first time unless my help is not enough the first time.

so try this and see if you get it. otherwise i will solve it.

for any body to roll, it requires a torque. this torque is usually provided by friction. so the friction b/w the plank and cylinder will casue the cylinder to

1) decelerate

2) roll in a clocwise sense.

friction will act to the left (all this in reference to your figure).

this friction stops acting when the cylinder stops rolling. so what will happen is that the VELOCITY  in the right direction will decrease, and at the same time the CLOCKWISE angular velocity will increase, until v =rw.

now the real problem is : will this v = rw before the cylinder falls off the plank or not?

the problem is very very long, and we will have to do this in 2 cases.

in the first case, we say that the cylinder continues to decelerate till the end. this is the easier case, so try it first. frictional force can be found, and use newtons second law and write torque equations. if the answer is absurd, like imaginary roots etc, then take second case.

assume that it decelerates for t seconds and from then v = rw..

well its long.. but this is the only method i know.

shit this question is a very long one. i guess you will be disappointed that i did not solve it.. and now that i see it i dont even want to.. lol.

shreyas