Calculate the relative angular velocity

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Homework Statement


AB is a rod of length 10 m that is leaning against the wall. Given variables are shown in the diagram. Find angular velocity of A wrt B.


https://imgur.com/a/8bEdYhN

I have a doubt in one step that I will highlight in "The attempt at a solution" part.

Homework Equations


angular velocity of A wrt B = relative velocity of A wrt B in perpendicular direction / Distance separating A and B

The Attempt at a Solution


Let velocity of B be 'v'.
I made components of velocities of A and B.
So, since the length of the rod remains the same, velocities along the rod should be same, i.e.,
10 root 3 Cos 60 = v Cos 30
I solved it and got v = 10 m/s

Since the velocity components that are perpendicular to line joining A and B are responsible for turning.

angular velocity of A wrt B = relative velocity of A wrt B in perpendicular direction / Distance separating A and B

Now here's my problem:
What is relative velocity of A wrt B in perpendicular direction?
I think it should be 10 root 3 Sin 60 - ( - 10 Sin 30) = 20 m/s
But our teacher did it like this : 10 root 3 Sin 60 - 10 Sin 30 = 10 m/s


And this same thing was done for two other questions. So is this just a mistake or is there some different concept when applying for relative velocity in case of angular motion?
 

Answers and Replies

  • #2
kuruman
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After some editing of previous posts, I agree with you. Both components of the relative velocity contribute positive terms in the direction perpendicular to the rod. Relative to point B, point A moves up and to the right.

Welcome to PF @Aamon.
 
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  • #3
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After some editing of previous posts, I agree with you. Both components of the relative velocity contribute positive terms in the direction perpendicular to the rod. Relative to point B, point A moves up and to the right.

Welcome to PF @Aamon.
Thank you for responding and welcoming me! :)
 

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