The velocity directions at points A, B and C are shown below.
The linear velocity of point A is,
Here, OA is the radius of the disc.
Substituting R for OA in the above equation, we get:
The direction of velocity at point A is tangential to the right direction.
The linear velocity of point B is,
Here, OB is the radius of the disc.
Substituting R for OB in the above equation, we get:
The direction of velocity at point B is tangential to the left direction.
The linear velocity of point C is,
Here, OA is the distance of point C from point O.
Substituting
The direction of velocity at point C is tangential to the right direction.
Since the disc is placed on frictionless table, it will not roll in the direction indicated. The velocity at the point of contact will not be zero in the absence of frictional force at the contact surface.