Instantaneous Centre Technique:

We have seen that a body undergoing plane motion contain two components:

1. Translational component, and

2. Rotation component.

Further, we may imagine a point (may be outside the body sometimes) about which the body appears to rotate, i.e. the translation motion of this point is zero. Such a point is called as instantaneous centre of rotation.

Consider a body undergoing plane motion. v_A and v_B are velocities of two points A and B at any instant as shown in Figure.

Draw perpendiculars to v_A at A and to v_B at B. These two perpendiculars meet at O. Then O is called as the instantaneous centre of rotation also known as instantaneous centre of zero velocity.

Then we have

v _A  = v_O  + v_OA           v_OA  = AO ω (Perpendicular to OA)

v _B  = v_O  + v_OB           v_OB  = BO ω  (Perpendicular to OB)

This is possible when v_O = 0 .

∴ O is instantaneous centre