RELATION BETWEEN LINEAR VELOCITY AND ANGULAR VELOCITY | |||

Consider a particle “P” in an object (in XY-plane) moving along a circular paths 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, q = DS / r DDividing both sides by Dt, we get Dq / Dt = (DS / r. Dt) r D q / Dt = DS/DtIf 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 w. _{ins}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 DV _{t} at the end of this interval will be | |||

DV _{t} = r Dw | |||

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 “. | |||

a_{t} = ra |

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