derivation of circular expression
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Explanation:
Deriving the centripetal acceleration formula
- We can calculate the arc length s as both the distance traveled (distance = rate * time = v Δt) and using the definition of a radian (arc = radius * angle in radians = r Δθ)
- The angular velocity of the object is thus v / r (in radians per unit of time.) ...
- Note the passing from sin to cos is via l'Hôpital's rule.
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A circular definition is one that uses the term(s) being defined as a part of the definition or assumes a prior understanding of the term being defined. There are several kinds of circular definition, and several ways of characterising the term: pragmatic, lexicographic and linguistic.
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