Rotational Dynamics
8.0 Instantaneous axis of rotation
8.0 Instantaneous axis of rotation
Instantaneous axis of rotation (IAR) is an axis of rotation about which the motion of a rigid body moving in plane motion is assumed to be pure rotational motion.
Note: Plane motion means combined translational and rotational motion.
The point of intersection of instantaneous axis of rotation with the plane of motion of the rigid body is called instantaneous centre of rotation (ICR).
About instantaneous centre of rotation all points of the rigid body are assumed to be moving in circles of different radii equal to their respective respective distance from the ICR with same angular velocity $\left( \omega \right)$ and angular acceleration $\left( \alpha \right)$ at that instant.
Rotational velocity of IAR $=0$
Translational velocity of IAR $=0$
So, total velocity of IAR $=0$ at that particular instant
IAR and ICR may lie inside or outside the rigid body.
Velocities of point $A$, $B$ and $C$ are the velocities due to their translational and rotational motion.
The concept of IAR & ICR is used to convert plane motion (i.e. combined translational and rotational motion) of a rigid body into pure rotational motion.
Angular velocity about the IAR or ICR is same as the original angular velocity of the rigid body.
For better understanding and simplicity, problems based on IAR and ICR can be solved by following two methods,
1. Geometrical method
2. Relative velocity method
