Calculate the relative angular velocity

In summary, 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. Given that the rod is at rest, the angular velocity of A is 10 m/s. However, because A is perpendicular to B, the angular velocity of A is 20 m/s.
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Aamon
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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.
8bEdYhN


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?
 
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  • #2
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
kuruman said:
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! :)
 

Related to Calculate the relative angular velocity

1. What is relative angular velocity?

Relative angular velocity is the measure of how fast an object is rotating with respect to another object, taking into account their relative positions and orientations.

2. How is relative angular velocity calculated?

Relative angular velocity is calculated by dividing the difference in angular displacement of two objects by the difference in time it took to make that displacement.

3. What are the units of relative angular velocity?

The units of relative angular velocity are radians per second (rad/s) or degrees per second (deg/s).

4. What is the difference between relative and absolute angular velocity?

Absolute angular velocity is the measure of how fast an object is rotating in an absolute frame of reference, while relative angular velocity takes into account the position and orientation of another object.

5. How does relative angular velocity relate to rotational motion?

Relative angular velocity is an important concept in rotational motion as it describes the speed and direction of rotation of an object with respect to another object. It can also be used to calculate other rotational properties such as angular acceleration and torque.

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