What is the derivation for v=rw?
Relation between linear velocity and angular velocity
Let ω→ Uniform angular velocity of point object moving along PQ
v → Linear speed
r → Radius of circular path
t → Time at which the object is at point P
t + Δt → Time at which the object is at Q
Let POQ = Δθ and
It means that an object describes an arc PQ of length Δl in time interval Δt.
From equations (i) and (ii),