Define angulnr velocity. Derive `v = r omega`

Explanation

Angular velocity (`omega` ): Rate of change of angular displacement is called angular velocity. Relation between linear velocity (v) and angular velocity `(omega)` : Let `alpha^1` particle P is moving along circumference of a circle of radius 'r' with uniform speed v. Let it is initially at the position A, during a small time `Deltat` it goes to a new position say C from B. Angle subtended during this small interval is say `dtheta` .

By definition angular velocity,
`omega = underset(Deltat to 0) (Lt) (Deltatheta)/(Deltat) = (dtheta)/(dt)`
But linear velocity v ` = underset(Delta t to 0) (Lt) (BC)/(deltat)`
When is small arc BC `= r d theta`
`rArr v = r. (dtheta)/(dt)`
`therefore v= r. omega (because (dtheta)/(dt) = omega)`