The family physician often provides the first and only medical intervention for fingertip injuries. Proper diagnosis and management of fingertip injuries are vital to maintaining proper function of the hand and preventing permanent disability. A subungual hematoma is a painful condition that involves bleeding beneath the nail, usually after trauma.
I think it's probably easier to flip the question, and find why angular velocity is equal to the linear velocity divided by the radius: [math]\omega = \frac{v}{r}[/math] From there, it's a simple algebraic manipulation.
Everything which turns or moves in the circular direction has both linear velocity and angular velocity. The angular velocity of a particle traveling on a circular path is defined as ratio of the angle traversed to the amount of time it takes to traverse that angle.