Relate rotational kinetic energy to potential energy

AI Thread Summary
The discussion centers on a physics problem relating rotational kinetic energy to potential energy, specifically addressing the change in height of a bar during its motion. The initial equation used was based on the full length of the bar, but the correct approach involves using the center of mass, which is at L/2, leading to a potential energy of mgL/2. This highlights the importance of considering the average change in height for the entire bar rather than just the end. Clarification was sought on why the center of mass is relevant, emphasizing that it represents the average position of the bar's mass. Understanding this concept is crucial for accurately calculating the energy transformations involved in the problem.
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Homework Statement


This problem is from the 2015 AP Physics C Mechanics free response, question 3 part b.
https://secure-media.collegeboard.org/digitalServices/pdf/ap/ap15_frq_physics_c-m.pdf
upload_2017-4-15_2-49-11.png


Homework Equations


K = 1/2Iω2
U = mgh

The Attempt at a Solution


The potential energy of the bar when it's horizontal gets transferred to kinetic energy when vertical, so I originally had the equation mgL = 1/2(1/3ML22
However, the scoring guidelines say that the change in height should be L/2, not L, resulting in a potential energy of mgL/2. Could someone explain why the change in height should be L/2 and not L?
 
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The change in vertical position of the end of the bar is L. Is that the point that's important in the problem?
 
vela said:
The change in vertical position of the end of the bar is L. Is that the point that's important in the problem?
It asks for the velocity of the "free end of the rod", so I think that it means the end of the bar. But why does the answer sheet say L/2 then?
 
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Is that relevant to the change in potential energy of the rod? Why not use the position of the other end or a point 1/3 the way in from one end? I'm trying to get you to think about what point is important when you talk about the potential energy of the rod.
 
vela said:
Is that relevant to the change in potential energy of the rod? Why not use the position of the other end or a point 1/3 the way in from one end? I'm trying to get you to think about what point is important when you talk about the potential energy of the rod.
So I have to take the entire bar into account and not just the end...kind of like taking the "average" change in height for all pieces of the rod?
 
Yes. More precisely, the average position of the mass of the bar, i.e., the center of mass.
 
vela said:
Yes. More precisely, the average position of the mass of the bar, i.e., the center of mass.
Okay, that makes sense. Thanks for the help!
 
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