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Moments of Inertia Derivation, Please Helpby Ush
Tags: moment of inertia 
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#1
Jun2710, 11:50 AM

P: 98

1. The problem statement, all variables and given/known data
I have attached the problem in one file and I have attached my attempt in the second file. I only need help deriving the moment of inertia for the first (1) and fourth (4) objects but I have attached my solutions to the other objects in case it helps jog someones memory onto how to do this =p 2. Relevant equations I = ∑m_{i}r_{i}^{2} A = area M = total mass dm = change in mass dA = change in area dr = change in radius 3. The attempt at a solution attempt is attached  Thank you for taking the time to read through my problem and helping me solve it, I appreciate your help 


#2
Jun2710, 12:05 PM

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P: 41,449

Number 1 is exactly the same problem as number 2, just with different limits of integration.
In number 4 note that all the mass is at the same distance from the axis. 


#3
Jun2710, 12:21 PM

P: 98

I'm not sure how to integrate one so that I'll get 1/12ML^{2}
I tried doing something similar dm/M = dr/0.5 L because dr starts from the pivot point in the center and max dr will only cover half of the total length. After doing the integration I didn't get 1/12ML^{2} I still don't understand how to begin the fourth one =[ 


#4
Jun2710, 12:37 PM

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P: 41,449

Moments of Inertia Derivation, Please Help



#5
Jun2710, 12:54 PM

P: 98

another attempt attached



#6
Jun2710, 01:21 PM

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P: 41,449




#7
Jun2710, 01:26 PM

P: 98

oh wow =o I can't believe I missed that.
Thanks so much! i understand how to do the first one now =) could you give me another hint onto how to do the fourth one? 


#8
Jun2710, 01:34 PM

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#9
Jun2710, 01:43 PM

P: 98

the distance from the axis of every element of mass, dm, is R ?
if R increases, the mass increases because you get a bigger shell dr/R = dm/M ?? =S 


#10
Jun2710, 01:50 PM

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#11
Jun2710, 01:58 PM

P: 98

R is constant for a given shell



#13
Jun2710, 02:17 PM

P: 98

if radius is constant. then mass is constant. there is no dr or dm =S
how do i sub dm for something? 


#14
Jun2710, 02:35 PM

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P: 41,449




#15
Jun2710, 02:39 PM

P: 98

if you have a constant then you take it out of the integral.
..oh my I = ∫R^{2} dm = R^{2}∫dm = R^{2} ∑m = R^{2}M THANK YOU SO MUCH! 


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