# RELATION BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY

 RELATION BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY Consider a particle “P” in an object (in XY-plane) moving along a circular path of radius “r” about an axis through “O” , perpendicular to plane of the figure i.e. z-axis. Suppose the particles moves through an angle Dq in time Dt sec. If DS is its distance for rotating through angle Dq then, Dq = DS / r Dividing both sides by Dt, we get Dq / Dt = (DS / r. Dt) r Dq / Dt = DS/Dt If time interval Dt is very small , then the angle through which the particle moves is also very small and therefore the ratio Dq /Dt gives the instantaneous angular speed wins. i.e. V = rw TANGENTIAL VELOCITY If a particle “P” is moving in a circle of radius “r”, then its linear velocity at any instant is equal to tangential velocity which is : V = rw TANGENTIAL ACCELERATION Suppose an object rotating about a fixed axis changes its angular velocity by Dw in time Dt sec, then the change in tangential velocity DVt at the end of this interval will be DVt = r D w Change in velocity in unit time is given by: DV / Dt = r. Dw / Dt if Dt approaches to zero then DV/Dt will be instantaneous tangential acceleration and Dw/Dt will be instantaneous angular acceleration “a “. at = ra