by Ush
Tags: moment of inertia
 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 = ∑miri2 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 Attached Thumbnails
 Mentor P: 40,251 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.
 P: 98 I'm not sure how to integrate one so that I'll get 1/12ML2 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 1/12ML2 I still don't understand how to begin the fourth one =[
Mentor
P: 40,251

 Quote by Ush I'm not sure how to integrate one so that I'll get 1/12ML2
You've already done the integral (in #2)--the only change is the limits of integration.

 I still don't understand how to begin the fourth one =[
I = ∫r2 dm. How does r vary as you move around the shell?
 P: 98 another attempt attached Attached Thumbnails
Mentor
P: 40,251
 Quote by Ush another attempt attached
For some reason, you are integrating from 0 to R/2. That's from the center of the rod to one end. But the rod goes from end to end.
 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?
Mentor
P: 40,251
 Quote by Ush could you give me another hint onto how to do the fourth one?
I thought I did:
 Quote by Doc Al How does r vary as you move around the shell?
I'll rephrase it. What's the distance from the axis of every element of mass dm as you go around the shell?
 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
Mentor
P: 40,251
 Quote by Ush the distance from the axis of every element of mass, dm, is R ?
Exactly. Is R a variable or a constant? (For a given shell.)
 P: 98 R is constant for a given shell
Mentor
P: 40,251
 Quote by Ush R is constant for a given shell
Right! So simplify and complete the integral: I = ∫R2 dm
 P: 98 if radius is constant. then mass is constant. there is no dr or dm =S how do i sub dm for something?
Mentor
P: 40,251
 Quote by Ush if radius is constant. then mass is constant.
Not sure what you mean. Hint: How do you deal with constants within the integral sign?
 P: 98 if you have a constant then you take it out of the integral. ..oh my I = ∫R2 dm = R2∫dm = R2 ∑m = R2M THANK YOU SO MUCH!

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