What is the derivation for v=rw - Physics - System Of Particles And Rotational Motion

Question

What is the derivation for v=rw?

Hansraj Rai · Accepted Answer

Dear Student!! Relation between linear velocity and angular velocity

Let Ï‰â†’ Uniform angular velocity of point object moving along PQ v â†’ Linear speed r â†’ Radius of circular path t â†’ Time at which the object is at point P t + Î”t â†’ Time at which the object is at Q Let POQ = Î”Î¸ and

It means that an object describes an arc PQ of length Î”l in time interval Î”t

Also,

From equations (i) and (ii),