Solving free-fall motion in a rotating frame through analogy with the electromagnetic problem

We present an undergraduate level solution for free-fall motion in a rotating frame under the action of the fictitious Coriolis force. This solution method is developed through analogy with the motion of a charged particle in uniform electric and magnetic fields. In particular, in a frame that drifts with the earth's rotation, the particle moves along a short arc of uniform circular motion perpendicular to the earth's angular velocity before hitting the ground. In the frame fixed on the earth, the circle becomes a cycloid, just as in the electromagnetic problem. Another advantage of this method is that a closed-form solution can be obtained even when air friction that is linear in the particle speed is included, which produces a transverse trajectory that is a logarithmic spiral in the drift frame. This approach gives students opportunities to review and apply previous knowledge such as charged particle motion, the harmonic oscillator, and frame transformations. It can also serve as the starting point for exploring more sophisticated solutions.