Obtain the relation between linear velocity and angular velocity
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Solution
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=△sr Dividing both side by △t △θ△t=1r△s△t In the time interval △t be infinitesimally small (△t→0), then lim△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=Vr V=rω In vector form, →V=→ω×→r