When we switch on an electric fan, we notice that its angular velocity goes on increasing. We say that it has an angular acceleration. We define angular acceleration as the rate of change of angular velocity. If ωi and ωf are the values of instantaneous velocity of a rotating body at instant ti and tf, the average angular acceleration during the interval tf – ti is given by
The instantaneous angular acceleration is the limit of the ratio as approaches zero. Therefore, instantaneous angular acceleration is given by
The angular acceleration is also a vector quantity whose magnitude is given by Eq. 5.5 and whose direction is along the axis of rotation. Angular acceleration is expressed in units of rad s-2.
Till now we have been considering the motion of a particle P on a circular path. The point P was fixed at the end of a rotating massless rigid rod. Now we consider the rotation of a rigid body as shown in Fig. 5.3. Imagine a point P on the rigid body. Line OP is the perpendicular dropped from P on the axis of rotation. It is usually referred as reference line.
As the body rotates, line OP also rotates with it with the same angular velocity and angular acceleration. Thus the rotation of a rigid body can be described by the rotation of the reference line OP and all the terms that we defined with the help of rotating line OP are also valid for the rotational motion of a rigid body. In future while dealing with rotation of rigid body, we will replace it by its reference line OP.
