If there is a ball on the ground initially at rest, Assume that the plane xoy(cartesian) is the ground and that Z is the normal of the ground.
If I spin the ball so that $\omega_x=\omega_y=0$ and $\omega_z$ has some value, how to calculate the effect of friction on the spin ? .
Assume we have the mass of the ball $m$ and its rotational inertia $I$ and the torque I applied on the ball to spin it is $\tau$, also assume that air resistance is negligible .
This is the problem, Now I know that the friction always oppose the relative motion but I don't exactly know how much the force will be and how to calculate resistant torque from that.
Not sure but I feel due to the fact that there is $\omega_z$ there is added Normal force from the ground because somewhat the ball moves towards the ground but that's wrong if $\omega_z$ is the same in direction as the Normal of the ground.
Also the speed of the contact point relative to the ground is zero because the contact point is part of the rotation axis, that's what confuses me : how is there a friction when there isn't any relative speed? is there "frictional torque" as opposed to "frictional force" or I'm wrong? please help me with this problem.