Simple arguments are presented that detectors moving with constant acceleration (even acceleration for a finite time) should detect particles. The effect is seen to be universal. Moreover, detectors undergoing linear acceleration and uniform circular motion both detect particles for the same physical reason. It is shown that the Unruh effect for a circularly orbiting electron in a constant external magnetic field used as a Unruh-DeWitt detector physically coincides with the experimentally verified Sokolov-Ternov effect.