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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. • Since v^2/r is centripetal acceleration, and v = (omega) x r, doesn't centripetal acceleration equal (omega) x v?

(centripetal acceleration is equal to (v/r) x r, and v/r = omega
(1 vote) • I do not understand what is meant by "and we typically view radians as an angle but if you think of it as an arc length, a radian you could view it as how many radii in length am I completing per second? And so, if I multiply that times the actual length of the radii, then you can get a sense of well, how much distance am I covering per second? "
(1 vote) • what is the difference between angular acceleration (alpha) and centripetal acceleration?
(1 vote) 