Elementary derivations of centripetal acceleration and works of Huygens and Newton: a revisit with a simple physical derivation

TL;DR

This paper revisits classical derivations of centripetal acceleration, relating them to Huygens and Newton's works, and introduces a more physically intuitive derivation method.

Contribution

It connects historical derivations with modern physical reasoning and presents a new, simpler derivation of centripetal acceleration.

Findings

Historical derivations are fundamentally related.

A more physically motivated derivation is proposed.

The approach simplifies understanding of centripetal acceleration.

Abstract

This work shows how two simple derivations of the centripetal acceleration are fundamentally related to seminal works of Huygens and Newton. A different, more physically motivated derivation is then given.