*Answer:* Let be the velocity of the cylinder's centre of mass,
the cylinder's angular velocity, the frictional force exerted by the
surface on the cylinder, the cylinder's mass, and the cylinder's moment of inertia.
The cylinder's translational equation of motion is written

Note that the friction force acts to accelerate the cylinder's translational motion. Likewise, the cylinder's rotational equation of motion takes the form

since the perpendicular distance between the line of action of and the axis of rotation is the radius, , of the cylinder. Note that the friction force acts to decelerate the cylinder's rotational motion. If the cylinder is slipping with respect to the surface, then the friction force, , is equal to the coefficient of friction, , times the normal reaction, , at the surface:

Finally, the moment of inertia of the cylinder is

The above equations can be solved to give

Given that (

which yields

Now, the cylinder stops slipping as soon as the ``no slip'' condition,

is satisfied. This occurs when

Whilst it is slipping, the cylinder travels a distance