Calculate the relative angular velocity

[Aamon]

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?

 

[kuruman]

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.

 

[Aamon]

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! :)