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Physics LibreTexts

23.4: Relations between Circular and Linear Motion

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It's a simple matter to derive some very useful relations between circular and linear motion. We begin with the relation between arc length s and angle θ (in radians) for a circle of radius r :

s=rθ

Taking the derivative with respect to time of both sides gives a relation between linear veloctiy v=ds/dt and angular velocity ω=dθ/dt :

v=rω


23.4: Relations between Circular and Linear Motion is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by LibreTexts.

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