# Two dimensional ball motion on a plane

Suppose i have a horizontal table. Choose a standard cartesian coordinate such that the $x-y$ plane coincise with the table. Assume that the table is not smooth. Suppose i have a solid ball with initial velocity $\vec{v} = (v_x,v_y,0)$ and The ball initially slipping with angular velocity $\dot{\theta} = (\omega,0,0)$.

How can i determine when the ball is not slip from the Newton's law and the torque equation ? This seems a bit complicated because now there is two friction force, first because the rotation of the ball and the second because the $x-$axis motion. This question is the extension of my answer in a question here.

• Related : Rotational physics of a playing card – sammy gerbil Nov 28 '17 at 16:11
• The ball will not slip, when the rotation of the ball due to the horizontal velocity equals the angular velocity. – Guill Dec 5 '17 at 7:25