Solving Dynamics Block Problem with Zero Force at Θ = 30 Degrees

[Torquenstein101]

I don't know if you guys can clearly see the image attached. (sorry i don't have my good digitial camera with me here). But the question is:

A 0.5 kg block B slides without friction inside a slot cut in arm OA which rotates in a vertical plane at a constant rate, (dΘ /dt) = 2 rad/s. At the instant when Θ = 30 degrees, r = 0.6 m and the force exerted on the block by the arm is zero. Determine, at this instant,
(a) the relative velocity of the block with respect to the arm
(b) the relative acceleration of the block with respect to the arm.
I believe I am on the right track and I did solve for the velocity of the block in transverse and radial terms. I got:
Vradial = (-0.6928) m/s and Vtransverse = (1.2) m/s
I have to find the velocity of the arm, and I did (not sure if its right), but my relative velocity is not coming out right...
Any help would be greatly appreciated.

 

[DLinkage]

I am extremely tired and have to goto bed, but I'll give you a hint for the vertical velocity. Imagine yourself attached to tube...how do you see the block move? The answer is simply in a straight line either towards or away from you depending on where you are standing. The idea here is that the velocity of the block with respect to an observer fixed in a rotating from with the tube will be purely radial. So if you place a unit vector radially outward from the pivot that rotates with the tube, the component of velocity in that direction is the velocity that the block will be obersved with if the observer is fixed to the tube.