centripetal acceleration formulas

[coach55]

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so the two formulas for centripetal acceleration are:
a = v^2 / r
and
a = omega^2 * r

How come the radius is directly proportional in one formula and inversely proportional in the other?

 

[Mithril]

Because in one you're dividing the square of a velocity by the radius, and in the other you're multiplying the square of a frequency by the radius. In either case, you end up with m/s^2.

If you want a completely thorough explanation, you'll need to look at the calculus for the equations' derivations.