Relativistic contraction of an accelerated rod

Abstract

The relativistic motion of an arbitrary point of an accelerated rigid rod is discussed for the case when velocity and acceleration are directed along the rod's length. The discussion includes the case of a time-dependent force applied to a single point, as well as a time-independent force arbitrary distributed along the rod. The time dependence of the rod's relativistic length depends on the application point of the force, but after the termination of acceleration the final velocity and length do not depend on it. An observer on a uniformly accelerated rod feels an inertial force which decreases in the direction of acceleration. The influence of non-rigidity of realistic rods on our results is qualitatively discussed.