Originally Posted by
Syn7
V^2/r is for uniform circular motion. It can also be re-written as 4pi^2r/T. T being the period is seconds, not delta t in seconds. It defines radial acceleration. But that is for an actual circle. When the curve is not uniform you have to either integrate or differentiate with respect to time. It gets complicated because as the curve changes the origin changes. And of course, it depends on which co-ordinate system you use.
The radius most certainly matters. Think about it this way... If you are doing a tight turn going 65 it feels more intense than doing a loose curve at that same speed. Smaller r = greater centripetal force. Which is defined as mv^2/r. It's Newtons second law. Worth reading up on if you're into that stuff. It never goes away. You start doing UCM and high school and it just gets deeper and deeper. Never ends.