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)?(adsbygoogle = window.adsbygoogle || []).push({});

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?

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# Radius as a function of Uniform Circular Motion

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