Consider a particle moving in a circle of radius ‘r’ with uniform angular velocity ‘ ω ’ and linear speed ‘V’. Let the particle moves from A to B in time ‘t’ seconds through a small distance ‘s’ on the circumference. Let θ be the angular displacement.
Angular velocity ω = \(\frac{\theta}{\tau} \)
Angular displacement \(\)θ = \(\frac{s}{\tau}\)
∴ ω = \(\frac{s}{\tau_{r}}\)
But \(\frac {s} {s}\)= v, linear velocity
∴ ω = \(\frac{v}{r} \,or\)
v = r ω
linear velocity = radius × angular velocity.