Relative Motion Is Solved by Shifting the Reference Frame
Motion depends on whose eyes you watch it through. Ride on one point (or body) and another point's velocity splits as vB = vA + vB/A; if that frame also rotates, the ω×r and Coriolis terms join in.
Two objects A and B each move. Riding on A, the velocity of B is vB/A = vB − vA. Drag B's heading and the vector joining the two arrow tips is exactly that relative velocity.
For two points on one rigid body, B's relative velocity is pure rotation perpendicular to the bar, ω×rB/A. So vB = vA + ω×r — A's velocity plus the rotation gives B's velocity as the diagonal.
Acceleration works the same way but splits into two pieces. The end of a bar pinned at A feels a tangential α×r (perpendicular to the bar) and a centripetal ω²r (inward). Raise ω and the centripetal term grows with ω squared.
When the frame itself rotates, one more term appears. A bead sliding on a rotating rod has absolute velocity equal to the rod's rotation ω×r plus the sliding vrel along the rod — this vrel is the new piece in a rotating frame.
Sliding in a rotating frame adds a term not just to velocity but to acceleration too — the Coriolis acceleration 2ω×vrel. An object thrown straight outward curving sideways is the proof, and the larger ω is, the more it curves.