Relative velocity

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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 \mathbf{v}_A and \mathbf{v}_B 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, or \mathbf{v}_{A \mathrm{\ rel\ } B}) is

\mathbf{v}_{A \mathrm{\ rel\ } B} = \mathbf{v}_A - \mathbf{v}_B.

Conversely, the velocity of B relative to A is

\mathbf{v}_{B \mathrm{\ rel\ } A} = \mathbf{v}_B - \mathbf{v}_A.

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.

[edit] References

  • Alonso & Finn, Fundamental University Physics ISBN 10:0-201-56518-8
  • 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.

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