Rolling and Slipping

Velocity Path
Voice Over Animation shows a disc rolling to the right on a horizontal surface. You can change the linear and angular velocities of the disc. You can use the check boxes in the display tab at the bottom right end to display the velocity vector of a point on the disc and/or the path traced by a point on the disc or see the motion without the clutter by turning them off. The velocity vector of the point due to rotation is displayed in red and the velocity vector due to translation is displayed in yellow. The green vector is the velocity vector of the point due to combined translation and rotation. When the disc reaches the right end of the animation area it stops.
Increase or decrease the linear/angular velocities and observe what happens. Try different combinations, finding the combination that causes the body to roll without slipping. Also observe the velocity vectors. The red and yellow vectors are parallel at the top most point and anti parallel at the bottom most point. Can you make out the ratio of the angular and linear speeds by observing the path? By observing the lengths of the velocity vectors?
Radius of the disc is assumed to be one unit.