Circular Motion 2

 ANGULAR ACCELERATION

The angular acceleration  of a rigid body is the rate of change of angular velocity of the body about the given axis of rotation.
If angular speed \(\omega\) of partilce P is not constant,i.e., at time t₁ angular speed is \(\omega_1\)  and at time t₂, angular speed is \(\omega_2\)  then this variation in angular speed in time interval (t₂-t₁)  gives rise to angular acceleration.The angular acceleration is defined as
                            \( \vec \alpha = \frac{{d\vec w}} {{dt}} = \frac{{w_2 - w_1 }} {{t_2 - t_1 }} \)
Since \(\omega\) is same for all particles in the rigid body. \(\alpha\)must also be the same as a consequence of above relations.Thus\(\alpha\) ,like\(\omega\) ,is a characteristic of the body as a whole.Its dimesions T^-2 are and units are taken to be \( rad/\sec ^2 \).The direction of angular acceleration is along the axis of rotation.
if the body is rorating in anti clock wise direction then angular acceleration is out side the plane of paper(along the axis of rotation it is in upward direction ,and can be taken as +ve).
if the body is rorating in clock wise direction then angular acceleration is in side the plane of paper(along the axis of rotation it is in downward direction ,and can be taken as -ve).