Angular Acceleration and Flow Rate Relationship

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SUMMARY

The discussion centers on the relationship between angular acceleration and flow rate in a buoyancy-based system. As the distance L increases, the moment exerted by the counterweight on the trunnion pin also increases, leading to a rise in angular acceleration according to the formula: sum of moments = moment of inertia x angular acceleration. However, the motion of the system is contingent upon the flow rate of water into the buoyancy chamber, which affects the buoyant weight. If the flow rate remains constant, the system's speed and acceleration will stabilize despite the increase in L.

PREREQUISITES
  • Understanding of angular acceleration and its relationship to moment of inertia
  • Familiarity with buoyancy principles and forces
  • Knowledge of fluid dynamics, specifically flow rate concepts
  • Ability to apply mathematical formulas related to rotational motion
NEXT STEPS
  • Explore the derivation of angular acceleration formulas in rotational dynamics
  • Study the principles of buoyancy and how they affect motion in fluid systems
  • Investigate the impact of flow rate on buoyant systems and their dynamics
  • Learn about the relationship between moment of inertia and angular motion in engineering applications
USEFUL FOR

Mechanical engineers, physics students, and anyone involved in the design or analysis of buoyancy-driven systems will benefit from this discussion.

VooDoo
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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?
 

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

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