Question

Find the relation between angular velocity and linear velocity of a body moving in uniform circular motion.

Answer 1

Let a body moves from point A to point B along the circular path. The angle sub tended by it is θ.
θ = arc/radius = x/r
x = r θ
Differentiate with time
dx/dt = d(r θ)/dt
Radius (r) is constant
dx/dt = r dθ/dt
v = r ω

Relation between angular velocity “ω” and linear velocity “v” is v = r ω