Intuitive Derivation of the Coriolis Force

TL;DR

This paper provides an intuitive derivation of the Coriolis acceleration, explaining the origin of the factor of 2 by combining velocity change in a rotating frame and geometrical rotation effects.

Contribution

It introduces a clear, intuitive derivation of the Coriolis force and explains the reason behind the factor of 2, which is often considered mysterious.

Findings

The Coriolis acceleration results from two distinct effects.

The factor of 2 arises from combining velocity change and geometrical rotation.

The derivation enhances understanding of non-inertial reference frames.

Abstract

The major difficulty when one teaches about non-inertial reference frames in undergraduate courses on Classical Mechanics is to find an intuitive way to derive the Coriolis acceleration. Indeed, there is a factor of 2 in the formula for the Coriolis acceleration and this factor is shrouded in mystery. In this paper we not only show an intuitive way to derive the Coriolis acceleration but we also show why there is a factor of 2. Indeed, it turns out that the Coriolis acceleration results from two completely different reasons (and hence the factor of 2). The first reason is this - as the particle moves to a new position, it `sees` a different local velocity of the rotating frame. The second reason is purely geometrical - the velocity vector is subjected to purely geometrical rotation due to the rotation of the reference frame. Both of these contributions unite and they result in the Coriolis acceleration.