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# Obtain the relation between linear velocity and angular velocity

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#### Consider a particle moving with uniform circular motion in anticlock wise direction with centre O and radius r the particle cover an arc of length △s in time △t moving from A to B.Hence the angular displacement is△θ=△srDividing both side by △t△θ△t=1r△s△tIn the time interval △t be infinitesimally small (△t→0), thenlim△t→θ△θ△t=1r[lim△t→θ△s△t]But lim△t→θ△θ△t=ω and lim△t→θ△s△t=V∴ω=VrV=rωIn vector form, →V=→ω×→r

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