Derive relation between linear velocity and angular velocity

Linear velocity is defined as the rate of change of displacement. The unit of linear velocity is m/s.

Angular velocity of a body is the rate of change of angular displacement over a period of time. The unit of angular velocity is rad/s.

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 angle POQ = Δθ

And,

It means that an object describes an arc PQ of length Δl in time interval Δt.

We know,

From equations (i) and (ii),

Direction of velocity at any point in circular motion is directed along the tangent to the circle at that point in the direction of motion.