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Disk rotation probelm 
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#1
Aug1414, 01:34 PM

P: 49

Ok here is the question that is being asked. Note that I know how to solve it one way, but when I go about trying to solve this problem another way that I think should give the the same result, I don't end up with the same result.
Question: A disk of mass M and radius R rotates at angular velocity ω0. Another disk of mass M and radius r is dropped on top of the rotating disk, in its center, causing both disks to spin at a new angular velocity ω. Assuming a negligible loss of energy to friction what is ω? Ok so this problem is pretty easy just set initial angular momentum to final angular momentum I(large disk)(ω0)=I(large disk)(ω)+I(small disk)(ω) and just solve for ω. which gives me an answer of ω=((R**2)ω0)/(R**2+r**2) So I know that is the correct answer. But then I also thought that I should be able to solve this using conservation of energy. I set this up like so (1/2)I(large disk)(ω0**2)=(1/2)I(large disk)(ω**2)+(1/2)I(small disk)(w**2) however when I solve I get ω=R(ω0)/sqrt(R**2+r**2) I checked my work multiple times and cannot find an error. I just don't know where my logic is going wrong. I mean if there is conservation of angular momentum doesn't that imply conservation of energy? Or since you are adding mass to the system can I not set up my energy conservation equation that way because I am not accounting for the rest energy of the second disk? I guess it is an inelastic collision when you drop the second disk on the top of the first so maybe that is why as well. But they say assuming a negligible loss to friction which throws me off. I mean isn't there significant loss of friction in inelastic collisions or do they just mean a small loss compared to the total rotational energy. Thanks for reading 


#2
Aug1414, 01:51 PM

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P: 41,579

Was that sentence really part of the problem? 


#3
Aug1414, 01:57 PM

P: 49

Yeah that's exactly what I was just thinking. Yeah it is a problem in a conquering the physics GRE book by Yoni Kahn and Adam Anderson. Well I guess not word for word. The last sentence is actually. "Assuming negligible a negligible loss of energy to friction, what is w?" I figured the first negligible was a typo.



#5
Aug1414, 02:04 PM

Mentor
P: 41,579

Check out the errata list: http://www.physicsgreprep.com/Errata_ed2_1.0.pdf
They recognize the error. 


#6
Aug1414, 02:05 PM

P: 49

Wait sorry I read wrong. It says "Assuming negligible a negligible loss of energy to friction, what is w?" I figured the first negligible was a typo but maybe my english reading is wrong and that changes the sentence.



#7
Aug1414, 02:06 PM

P: 49

AHH THANK you sooo much. You just solved another problem I had with the book as well that I thought was weird!!!! Just solved two problems that I was stuck on. Saved me from posting for the other. Thanks so much!



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