Relation between Linear and Angular Quantities of Motion

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