Question

How is instantaneous velocity of any particle of a rolling disc perpendicular to the point of contact with the ground?

Answer 1

Answer:

It is because you have assumed that the circular disc is a rigid body and the whole disc is instantaneously rotating about the point of contact P0.

Part of the disc which I shall call "Rod" P2P0 is rigid and instantaneously rotating about point P0 which means that the velocity of any point on the "rod", eg v⃗ 2, must be perpendicular to radial vector P0P2→.