I am dealing with a question that has me puzzled. Suppose an object which is rolling on a horizontal plane, with initial linear velocity $v=v_0$ and angular velocity $\Omega=\Omega_0$.
There is friction between the object and the floor, but we are not considering aerodynamic friction (i.e., no air). Intuition tells me that after a while the object will stop, i.e., it won't rotate nor move anymore. But that seems to be impossible!
Consider the first possibility: friction pointing backwards.
$F_r$ would make the object stop moving in the horizontal direction.. but the induced torque would make $\Omega$ increase!
The second possibility is that $F_r$ points forwards. That would cause the object to stop rotating, but it would accelerate it in the horizontal direction.
So.. the only possible option left is that $F_r = 0$, and that the object will continue to move and rotate for ever. That seems really unintuitive to me. Is there something I'm missing?
Just to clarify, I'm not imposing any additional conditions on the problem, such as rolling without slipping.