Consider a body moving along a circular path from A to B as shown in fig:
Let, r = Radius of the circular path
θ = Angular displacement in radians
s = Linear displacement
v = Linear velocity
ω = Angular velocity
a = Linear acceleration
α = Angular acceleration
From the geometry of the figure, we know that
s = r.θ
We also know that the linear velocity,
v = ds/dt = d(r.θ) / dt = rx dθ/dt = r.ω
a = dv/dt = d(r.ω)/dt = rxdω/dt = r.α