Instant centers: rolling contact

Rolling without slipping

For a wheel rolling without slipping on a fixed surface, the contact point of the wheel with the surface is zero. Therefore, the velocity of the contact point is zero. The velocity of any point on the wheel is in a direction perpendicular to the line connecting that point with the contact point. This is as shown in the video below.

 

Rolling with slipping

Compare this with the video below when the wheel slips as it rolls; in this case, the contact point is NOT the instant center. (The animation shows that the velocity of point C is NOT zero when it is in contact with the ground.) Where is the instant center for rolling with slipping? How would you find this point? HINT: The IC of the wheel lies on both the perpendicular to the velocity of O and the perpendicular to the velocity of C when it is in contact with the ground - where do these two perpendiculars intersect?