Finding angular velocity of telescopic arm

[berdan]

Homework Statement

So ,here is the question : The structure is shown in the picture.
All I need is to find the angular velocity of telescopic arm BC ,in this current position.

http://img197.imageshack.us/img197/3954/w6e.JPG

Homework Equations

Well,them simple ω=rXv/r$\bullet$r

The Attempt at a Solution

Here is my attempt,and I don't know why it is wrong .

I said that ω$_{bc}$=ω$_{b}$-ω$_{c}$

Then I calculated ω$_{b}$=rXv/r$\bullet$r , same with ω$_{c}$ .
The velocity of those points were simply r*ω of the joints.
I set the coordinates O point in the lower left corner . Anyway,I got the correct angular velocities next to that system of coordinates.
But when I tried to say ω$_{bc}$=ω$_{b}$-ω$_{c}$ , I got the wrong answer .
Why is that ?
What is the correct way to look at that problem ?

Thanks in advance.

 

[KataKoniK]

Thank you for your question. I can see that you have already made an attempt at finding the angular velocity of the telescopic arm BC, but your approach may not be entirely correct.

Firstly, let's define the angular velocity of a body as the rate of change of its angular position with respect to time. In this case, we are looking for the angular velocity of the telescopic arm BC, which is rotating around the point B. Therefore, we need to find the angular position of the arm BC with respect to time.

As you correctly stated, the angular velocity of a point on a rotating body is given by the cross product of its position vector and its linear velocity. However, in this case, we need to consider the velocity of the arm BC as a whole, rather than just the velocities of points B and C.

To find the velocity of the arm BC, we can use the concept of relative motion. The velocity of point B is known, and we can calculate the velocity of point C relative to point B using the velocity addition formula. Once we have the velocity of point C relative to point B, we can then use the same formula to find the velocity of the arm BC relative to point B.

Once we have the velocity of the arm BC, we can then use the same approach as you did to find its angular velocity. However, we need to be careful with our coordinate system. It is important to note that the angular velocity of a body is independent of the coordinate system chosen, but the components of the angular velocity vector will change depending on the chosen coordinate system.

In this case, it may be helpful to choose a coordinate system with the origin at point B, as this will simplify the calculations. Once you have found the angular velocity of the arm BC, you can then convert it to the desired coordinate system by using the appropriate transformation equations.

I hope this helps. Good luck with your calculations!