Rotational motion, frictionless.

http://img444.imageshack.us/img444/8148/rollwx.jpg [Broken]

A rope is wound around a cylinder of mass 4kg, and I=0.02kg.m2 about the cylinder axis.
The frictional force between table and cylinder is negligible.

Solution:
a=20/4=5.0m/s2
α=ar is not applicable when slippage occurs.

My question.
1.Is the cylinder moves forward with acceleration a without any rotation.
2. Is Fr=Iα is still applicable in this case, even though we know α=ar not applicable.
3. If we play yo-yo in zero gravity environment,how does the yo-yo behave when we pull it?

Thank you.

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K^2
1. No, see 2.
2. Yes, Fr=Iα is always applicable. α=ar constraint is only needed for rolling, and is achieved via additional force, that being the force of friction. When no friction is present, you just compute angular and linear accelerations separately.
3. Yo-yo in zero-g will behave exactly the same as this test case. It will accelerate and spin in direction it's being pulled.

Thank you.
That really helpful since the book didn't say about rotation only a=αr is not applicable.

haruspex