# Obtain the relation between linear velocity and angular velocity

#### 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