# Relative angular velocity in a rotating rod

Consider a rod AB rotating about one of it's end A with angular velocity w.
Now angular velocity of each point of the rod is same i.e. w.
But if we have to find the relative angular velocity of the end B w.r.t. mid point of rod, what it will be?

Will it be zero because, w-w=0

or first we have to find the velocity of end B which is wR(R is length of Rod)
then find velocity of mid-point wR/2 and then find relative velocity of end B w.r.t. to mid point which is
wR-wR/2=wR/2
then divide it by distance between B and mid point which is R/2 and get relative angular velocity which now comes out to be w.

Which method is right and why the other method is wrong?

Svein
Now angular velocity of each point of the rod is same i.e. w.

But why two answer are coming through different method?

phinds
Gold Member
2021 Award
Make your xy coordinates at the end that is stationary. Clearly, as you say, the other end is rotating in that frame of reference.

Now make your xy coordinates with the x axis along the rod and the y axis perpendicular to that. Are any points on the rod rotating in that frame of reference?

Make your xy coordinates at the end that is stationary. Clearly, as you say, the other end is rotating in that frame of reference.

Now make your xy coordinates with the x axis along the rod and the y axis perpendicular to that. Are any points on the rod rotating in that frame of reference?
I didnt get you. Sorry :(