Find the instantneous axis of rotation of a rod length l when its end A moves with a velocity vecv_(A)=hati and the rod rotates with an angular velocity vecomega=-v/(2l)hatk.

Find the instantneous axis of rotation of a rod length l when its end

1.	Find the instantneous axis of rotation of a rod length l when its end A moves with a velocity vecv_(A)=hati and the rod rotates with an angular velocity vecomega=-v/(2l)hatk.
Answer» Solution :Let us choose the POINT `P` as `ICR` in the extended rod. We can say `ICR` is a point of zero VELOCITY. So we can write `vecv_(P)=vecv_(P,A)+vecv_(A)` we have `vecv_(P)=0` Hence `vecv_(P,A)=vecv_(A)=0` Here `vec_(A)=vhati` and `vecv_(P,A)=-omegahati` Hence `-omegarhati+vhati=0` `implies v=omegar` or `r=v/omega=v/((v/2l))=2l` Hence `ICR` will be LOCATED at a DISTANCE `2l` from `A`. Method 2 The instantaneous centre of rotation will be lie on the perpendicular line at point `A` with `vecv_(A)`. The `ICR` will lie at distance `AP+(\|vecv_(A)\|)/omega=v/(v/2l)=2l` or at a distance `2l` from point `A`.