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