How exactly does radius affect centripetal acceleration? In one formula we have (a=v^2/r) which implies inversely proportional, while in the other we have (a=(w^2)*r) which implies directly proportional. I understand that increasing r increases velocity (v=w*r) which means the right answer is increasing r increases acceleration, however how do we justify that increasing r would decrease a in the formula (a=v^2/r)? Also how can I intuitively makes sense of this? Does increasing r not mean that the same velocity has more time to change (as Khan Academy states at 3:29-4:32) --> This MIT lecture at 5:40-6:21, states that the acceleration would decrease as radius decreases. http://www.youtube.com/watch?v=Otmg0-knGtE&list=ECF688ECB2FF119649 So which is it ? They seem to be saying opposite things. Am I misunderstanding something? p.s. this site is amazing that people contribute their time and knowledge for free to help someone else they will never meet in their life. Truly thank you from one sentient being to another.