The horizontal components of velocities of two points in a rigid body must be equal but can we conclude that vertical velocities have to be equal?

Question

Consider two points in a rigid body and their velocities at a particular angle to the horizontal. The horizontal components of velocities must be equal so as to satisfy the basic definition of a rigid body. Can we also say that their vertical components must be equal so as to maintain the gap?

Answer 1

Neither the horizontal nor vertical components of the velocities must be the same to satisfy the rigid body constraints. If the body is rotating, the velocities at different distances from the center of the rotation will be different.