## 9677 | Problem Number: 32

jax
Posts: 4
Joined: Wed Nov 23, 2005 12:26 am

### 9677 | Problem Number: 32

I am having trouble solving this problem. I know the answer is B (from http://grephysics.net/disp.php?yload=pr ... bmit=Go%21) but I don't understand the solution. Here is what I am getting.

For I_A I am getting 3mr^2.
Since r = l/sqrt{3}, I_A = ml^2. This is consistent with the answer at grephysics.net.

for I_B I am trying to get it with the parallel axis theorem (I = I_center + md^2). In this case, I_center =I_A = ml^2, and d is the distance between the two axes (A and B) which is equal to r, and as before r=l/sqrt{3}.

So= I_B = I_A + mr^2 = ml^2 + ml^2 / 3 = 4ml^2 / 3 . This is different from the answer on grephysics.net but it seems like it should be right. What am I doing wrong? Why is I_B actually equal to I_A.

Any help would be much appreciated. Thanks!

-Jax

yosofun
Posts: 87
Joined: Mon Oct 31, 2005 5:50 am
hi jax,

i've posted a clarification in the solution on the link above.

note that there are 3 masses so the parallel axis theorem should be I_b=I_{cm} + 3md^2, where d is the displacement of axis from center of mass.

So, I_b=I_a+3ml^2/3 = 2ml^2

yosun

jax
Posts: 4
Joined: Wed Nov 23, 2005 12:26 am
Thanks a lot ! I didn't post on the other site because I thought nobody would notice it (unless they happened to check the solution to that question after I posted). I did not learn much about moments of inertia or the parallel axis theorem in my undergraduate studies, so this question really confused me (and it seems that I can only find very basic explanations / formulas for the parallel axis theorem).

thanks again,
-Jax

yosofun
Posts: 87
Joined: Mon Oct 31, 2005 5:50 am
hi jax,

a good book on the parallel axis theorem in a more general nature would be Marion and Thornton's Classical Dynamics (or Goldstein's book)

Beer and Johnson's Statics and Dynamics for Engineers offers a lot of examples, problems and answers on parallel axis theorem, inertia, and other aspects of mechanics.

also -- i tend to check the comments part of http://grephysics.net multiple times a day. if you post there, i should be able to answer your question faster (in general). (also, future test-takers with the same problem would not have to google search for alternate solutions and clarifications if all elements of the problem were concentrated in one place.)

fyi: the top 10 latest comment postings are listed on the frontpage of the site (it's right below the MetaSearch). i'm working on interviewing some others to be authorized moderators on the site, so that questions might be answered within the hour.

jax wrote:Thanks a lot ! I didn't post on the other site because I thought nobody would notice it (unless they happened to check the solution to that question after I posted). I did not learn much about moments of inertia or the parallel axis theorem in my undergraduate studies, so this question really confused me (and it seems that I can only find very basic explanations / formulas for the parallel axis theorem).

thanks again,
-Jax