Angular Acceleration and Flow Rate Relationship

[VooDoo]

Hey guys,

Thanks for all the replies. I ended up having the test for this subject and the question was a bit different to what I was expecting. I have attached an image similar to that of the test question.

Basically the question asked to explain what would happen to the angular acceleration (which is not constant) of the bar as the distance L increased.

When I used the formulas they showed that as the distance L increased the moment the counterweight exerted on the trunnion pin increased. I know the formula: sum of moments=moment of inertia x angular acceleration. So that would mean the angular acceleration of the bar would increase?

The system works on the basis that Wc is just heavy enough to overcome S & W, however with the buoyant weight there, the system will not move. As the buoyant chamber fills up with water the buoyant weight due to buoyancy forces lifts and the gate slowly begins to move.

So my argument was, that even though the L length was increased and hence angular acceleration (which is not constant in the system) would increase the motion of the system would depend on the flow rate of water into the buoyancy chamber.

Thus if the same flow rate was maintained, the buoyant weight would move upwards with the same velocity and thus the system would move with the speed/acceleration as before?

So the class was divided 50/50…just wondering what you guys think?

 

[nvn]

Fill in your equation in paragraph 3, then solve for angular acceleration, alpha, to see what happens to alpha as a function of L.

 

[Mene]

It's great to see that you are actively engaging with the material and thinking critically about the question. It seems like you have a good understanding of the concepts involved and your reasoning is sound. However, it's difficult to say for sure without seeing the specific diagram and equations used in the question.
In general, when the distance L increases, the moment of inertia of the bar will also increase, which means that a greater force will be required to rotate it. This could result in an increase in angular acceleration, but as you mentioned, the flow rate of water into the buoyancy chamber also plays a crucial role in determining the motion of the system. It's possible that the increase in angular acceleration could be counteracted by a decrease in flow rate, resulting in the system moving at a similar speed/acceleration as before.
Ultimately, the correct answer would depend on the specific details of the question and the system being studied. It's important to carefully consider all factors and variables when analyzing a situation like this. Keep up the critical thinking and good luck on your test!