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# Deriving formula for centripetal acceleration from angular velocity

Deriving formula for centripetal acceleration in terms of angular velocity. using linear speed formula.

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• I understand that centripetal acceleration is what causes change in the constant velocity direction, which altogether allows for circular motion. So is there a specific magnitude of centripetal acceleration required for every specific constant velocity value for an object to go in a circle?

And how does the change in the magnitude of centripetal acceleration affect motion? Since tangential velocity is what accelerates the object going around in a circle, would changing centripetal acceleration magnitude simply affect the path of the object? Example being if it is insufficient, an object then will follow something like an elliptical trajectory or even a straight-line path because acceleration is no longer enough to maintain circular motion. • Derivation of centripetal acceleration • ...So is the centripetal acceleration directly or inversely proportional to the radius of the circular path, since ac=v^2/r=w^2*r.In the first scenario, ac is inversely proportional to the radius, whereas, in the second scenario, ac is directly proportional to the radius of the circular path. Please enlighten me.   