Derive an equation for centripetal acceleration
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Naveen Sharma 8 years, 3 months ago
Consider the distance traveled by the body over a small time increment Δ<i>t</i>:
We can calculate the arc length <i>s</i> as both the distance traveled (distance = rate * time = <i>v</i> Δ<i>t</i>) and using the definition of a radian (arc = radius * angle in radians = <i>r</i> Δ<i>θ</i>:)
The angular velocity of the object is thus <i>v</i> / <i>r</i> (in radians per unit of time.)
The right half of the diagram is formed by putting the tails of the two <i>v</i> vectors together. Note that Δ<i>θ</i> is the same in both diagrams.
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