Two dimensional motion includes both a translation and rotation components. To solve problems, it is usually easier to break rigid body motion into these two components.

To derive the 2D relative velocity equation, first relate two arbitrary points on a rotating body,

     r_B = r_A + r_B/A

Differentiating with respect to time gives

     dr_B /dt = dr_A /dt + dr_B/A /dt

The relative velocity equation can be separated into linear motion and angular motion,

The rotation equation can also be written as

     v_B = v_A + ω × r_B/A

     v_B = v_A + ωre_t