Solve Dynamics Problem Involving Block & Arm Rotation

[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.

***EDIT***
Never mind, I think I got it... Vradial= 1.226 m/s and Vtransverse = 1.2 m/s

 

[lippyka]

The relative velocity of the block with respect to the arm is thus 1.226 m/s.The relative acceleration of the block with respect to the arm is equal to the angular acceleration of the arm times the radius of the arm, which is 0.6 m. Therefore, the relative acceleration of the block with respect to the arm is 2 rad/s^2 * 0.6 m = 1.2 m/s^2.

 

[kyle8921]

I would provide the following response:

Thank you for sharing your work and progress on solving this dynamics problem involving a block and arm rotation. It seems like you are on the right track and have solved for the velocity of the block in transverse and radial terms. It is important to double check your calculations and make sure they are correct.

To determine the velocity of the arm, you can use the equation v = rω, where v is the velocity of the arm, r is the distance from the center of rotation to the block, and ω is the angular velocity. In this case, the distance r is 0.6 m and the angular velocity ω is 2 rad/s. Plugging these values into the equation, we get v = 0.6 m * 2 rad/s = 1.2 m/s.

As for the relative velocity of the block with respect to the arm, it can be calculated by subtracting the velocity of the arm from the velocity of the block. In this case, the relative velocity would be (1.226 - 1.2) m/s = 0.026 m/s.

To find the relative acceleration of the block with respect to the arm, you can use the equation a = rα, where a is the acceleration of the block, r is the distance from the center of rotation to the block, and α is the angular acceleration. Since the angular acceleration is constant at 0, the relative acceleration would be 0 m/s^2.

I hope this helps and good luck with your further calculations. Remember to always double check your work and make sure your units are consistent.