6.Angular Displacement , Angular Velocity and Angular Accelearation

Angular Displacement , Angular Velocity and Angular Accelearation Consider a rigid body which is circulating about an axis. In this body each particle also rotating about the same axis. We just consider motion of one particle and generalize it to the whole rigid body.

A particle ‘P’ is moving around an axis with the uniform linear velocity v in a circle. In t time it goes from point A to B. It travels a distance x from A to B. Angle AOB is d so it travels by an angle d
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d is the angular displacement of the particle in t time.
It is a vector quantity and its S.I. unit is radian. Angular velocityThe rate of change of angular displacement is known as angular velocity and it is denoted by  . So for small time dt .

it is a vector quantity and its S.I. unit is radian/sec.



d dt

Angular velocity will be same for all particles in the rigid body as all particle rotate along the same rotation axis. If R=0 then v=0 The direction of angular velocity can be found by screw rule or right hand thumb rule. In above figure direction of angular velocity is upward because particle rotating anti clock wise.

Angular accelerationRate of change of angular velocity is called angular acceleration and it is denoted by  -



d dt
2

It is vector quantity and its unit is radian/ sec Its direction will be in the direction of torque.

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