Hi all. Reading on several books and papers, I found that the motion of a wheel moving on a flat surface are given by (assume that positive torques are counter-clockwise and the positive direction of the motion is toward the right direction): m \dot v=F J \dot ω=-rF+T for T<0, where m is the wheel mass, J is the wheel inertia, F is the tractive force due to the sliding friction, r is the wheel radius and \dot z indicates the time derivative of z and T is the applied torque to the wheel, and m \dot v=-F J \dot ω=rF+T for T>0. Now assume to start with the same initial condition v0=ω0 and assume to apply a sufficiently large (in absolute value) T<0 for t0≤t<t1. The system evolves accordingly to the first equations, and, at time t=t1, I would have |v(t1)|<|rω(t1)|. Now, assume to apply a sufficiently small torque T>0. The system now evolves accordingly to the second dynamics. However, there will be a time t=t1 such that v(t1)=0 and rω(t1)≠0. This means that the wheel stop to translate but it doesn't stop to roll. Does it make sense physically? I struggled a lot to think about an everyday example which exhibit this phenomenon but I cannot find one, and I wonder if there is some mistake in my reasoning.