Physics Blog Number 7 - July 2, 2013

Centripetal acceleration

It's been a while, over a year and a half, since I've had time to put down the results of my "investigations."

My latest "discovery" has been different ways of deriving centripetal acceleration.  So far, I have found 6 distinct methods, all of which have a neat twist to them, and all give a deeper understanding of what was a very difficult concept back in the 17th century.  Here are my versions of the derivations.

This started several years ago when I ran across an neat derivation (Method #5) in Landau's book "General Physics," that he wrote with Akhiezer and Lifshitz.  Then, more recently, I read this article in The American Journal of Physics, titled "Circular motion," by RC Henry. He showed a neat method by Newton that was far simpler than the one Huygens had originally used (Method #2).

After working through all of them, I think that my favorite is still that of Landau - it's clean and elegant. But it requires a fairly sophisticated theory of vectors, which Huygens didn't have, and therefore didn't use.