A massless rope is wrapped several times around a solid cylinder of radius R = 20 cm and
mass M = 20 kg, which is at rest on a horizontal surface.
Someone pulls 1 m of the rope with a constant force of 100 N, setting the cylinder in motion.
Assuming that the rope neither stretches nor slips and that the cylinder rolls without slipping,
what is the final angular velocity of the cylinder and the speed at its surface?
The moment of inertia of a cylinder of mass M and radius R is MR2/2.
The Attempt at a Solution
I've used conservation of energy to write that Fx=0.5*m*w^2*R^2+0.5*0.5*m*R^2*w^2=0.75*m*R^2*w^2.
Obviously I'd rearrange this for w, but I don't know how to find x. The question says that 1m of rope is pulled off the cylinder, but how do I find the distance that the cylinder travels in this time? I realise this is probably obvious