Relative Motion In a Plane

Just as in rectilinear relative motion, the motion of two particles moving in plane curvilinear motion can be related. However, we must now use vector notation, since the motion is no longer constrained to a straight line.

Therefore, the position, velocity, and acceleration of particle B relative to the particle A are given by

Recall that position depends upon origin location of the coordinate system, while velocity and acceleration are independent of the origin location. Therefore, the velocity (and acceleration) of particle B measured relative to particle A is just the difference in the absolute velocities (and accelerations).

These vectors can be used in any convienent coordinate system: (x,y), (n,t), or (r,).