Simple quantitative examples illustrating how the centrifugal and Coriolis forces ‘rescue’ Newton’s second law in rotating frames

This paper is prepared for those who have already learned the physics of circular motions and the centripetal force and are curious about the centrifugal and Coriolis forces. Instead of deriving them or exploring the theory, we aim to bring forward several quantitative examples to illustrate what conceptually they are, along with evidencing the notion that ‘Newton’s second law in rotating reference frames holds only when the centrifugal and Coriolis forces are in action’. All our examples involve mostly circular motions, and, most importantly, our approach to dealing with the frame transformation is without using the equations and purely on a qualitative argument basis.