Relative angular velocity in a rotating rod

AI Thread Summary
In a discussion about the relative angular velocity of a rotating rod, two methods were proposed to determine the relative angular velocity of point B with respect to the midpoint. One method suggests that the relative angular velocity is zero since both points share the same angular velocity, while the other method calculates it as w by finding the velocities of both points and their distance apart. The confusion arises from differing interpretations of the reference frame and the nature of angular velocity in a rotating system. Clarification on the coordinate system and the motion of points in that frame is essential for resolving the discrepancy. Understanding these concepts is crucial for accurately determining relative angular velocities in rotational dynamics.
TyrionTestBok
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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?
 
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TyrionTestBok said:
Now angular velocity of each point of the rod is same i.e. w.
You seem to have answered your own question.
 
Svein said:
You seem to have answered your own question.
But why two answer are coming through different method?
 
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?
 
phinds said:
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 :(
 

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