Relative velocity
In kinematics, relative velocity is the vector difference between the velocities of two objects, as evaluated in terms of a single coordinate system, usually an inertial frame of reference unless specifically stated otherwise.
For example, if the velocities of particles A and B are vA and vB respectively in terms of a given inertial coordinate system, then the relative velocity of A with respect to B (also called the velocity of A relative to B) is vA – vB. Conversely the velocity of B relative to A is vB – vA. If no other system of coordinates is specified, the expression “velocity of A relative to B” is usually understood as shorthand for “the velocity of A in terms of an inertial coordinate system with respect to which B is at rest”.
In Galilean kinematics (i.e., not accounting for the effects of special relativity), the relative velocity between two particles is the same with respect to any system of inertial coordinates. This is because changing from one inertial coordinate system to another (according to Galilean kinematics) simply adds a common increment vector to each velocity vector, so the difference between any pair of velocities is unaffected. However, taking the effects of special relativity into account, the relative velocity between two particles actually depends on the inertial coordinate system in terms of which the individual velocities are evaluated. This is because the effect of changing from one system of inertial coordinates to another is more complicated than simply adding a common increment vector to each velocity vector.
References
- Alonso & Finn, “Fundamental University Physics“ Volume 1 , Addison-Wesley.
- Greenwood, Donald T, “Principles of Dynamics”.
- Goodman and Warner, “Dynamics”.
- Beer and Johnston, “Statics and Dynamics”.
- McGraw Hill Dictionary of Physics and Mathematics.
- Rindler, W., “Essential Relativity”.