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    • https://phys.libretexts.org/Courses/Prince_Georges_Community_College/General_Physics_I%3A_Classical_Mechanics/23%3A_Circular_Motion/23.04%3A_Relations_between_Circular_and_Linear_Motion
      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 \(\theta\) (in radians) for a circle of radi...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 \(\theta\) (in radians) for a circle of radius \(r\) : \[s=r \theta \text {. }\] Taking the derivative with respect to time of both sides gives a relation between linear veloctiy \(v=d s / d t\) and angular velocity \(\omega=d \theta / d t\) : \[v=r \omega\]

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